Module 2
Understanding Risk Assignment
a. Defining Risk
The dictionary definition of risk, the “possibility of loss or injury,” highlights
the perils of putting oneself in a situation in which the outcome is unknown. But this
common use of the word doesn’t quite fit our purposes because we care about gains as
well as losses. We need a definition of risk that focuses on the fact that the outcomes
of financial and economic decisions are almost always unknown at the time the
decisions are made. Here is the definition we will use: Risk is a measure of
uncertainty about the future payoff to an investment, assessed over some time horizon
and relative to a benchmark. This definition has several important elements. First, risk
is a measure that can be quantified. In comparing two potential investments, we want
to know which one is riskier and by how much.
When considering the desirability of various investments, one key principle
holds true: all other factors being equal, investments that carry higher levels of risk
are generally less appealing to investors. This is because riskier investments come
with a greater potential for loss, making them less attractive compared to safer
alternatives. Investors typically seek to minimize their exposure to risk while
maximizing their potential returns. Consequently, the heightened risk associated with
certain investments necessitates a lower price to entice potential investors. This lower
price acts as a form of compensation for the increased risk they are taking on.
To elaborate, riskier investments require a higher rate of return to justify the
potential for greater losses. For instance, consider a hypothetical scenario where an
investor is choosing between two investment opportunities. The first investment is
relatively safe with a predictable and steady return, while the second investment is
much riskier with a volatile return profile. Rational investors will likely favor the
safer investment unless the riskier one offers a significantly higher potential return to
compensate for the additional risk. This is why riskier investments tend to have lower
initial prices or higher yields—they need to provide an incentive for investors to
accept the additional risk.
Moreover, the pricing of investments is intricately tied to the quantifiable
aspects of risk. Risks that can be measured and quantified, such as credit risk, market
risk, and liquidity risk, can be incorporated into pricing models. Financial analysts
and investors utilize various tools and techniques, such as discounted cash flow
analysis, option pricing models, and risk-adjusted return metrics, to assess and price
these risks. However, uncertainties that are not quantifiable present a unique
challenge. These uncertainties, often referred to as "Knightian uncertainty" after the
economist Frank Knight, cannot be easily incorporated into traditional pricing models
because they lack a statistical basis for measurement.
Knightian uncertainty encompasses factors such as geopolitical events, natural
disasters, or unprecedented market disruptions, which are inherently unpredictable
and cannot be quantified in terms of probability. Since these uncertainties cannot be
accurately priced, they introduce an element of ambiguity that complicates investment
decisions. Investors may respond to unquantifiable uncertainties by demanding an
additional risk premium or by avoiding certain investments altogether, leading to
market inefficiencies and pricing anomalies.
In summary, the interplay between risk and return is a fundamental concept in
investment decision-making. Riskier investments are less desirable to investors and
command lower prices or higher yields as compensation for the additional risk. While
quantifiable risks can be incorporated into pricing models, unquantifiable
uncertainties pose a significant challenge, often leading to greater caution and demand
for risk premiums among investors.
Second, risk arises from uncertainty about the future. We know that the future
will follow one and only one of many possible courses, but we don’t know which one.
This statement is true of even the simplest random event—more things can happen
than will happen. If you flip a coin, it can come up either heads or tails. It cannot
come up both heads and tails or neither heads nor tails; only one of two possibilities
will occur. Third, risk has to do with the future payoff of an investment, which is
unknown. Though we do not know for certain what is going to happen to our
investment, we must be able to list all the possibilities. Imagining all the possible
payoffs and the likelihood of each one is a difficult but indispensable part of
computing risk.
Fourth, our definition of risk encompasses not just a single investment but also
a group of investments. This broad interpretation allows us to consider a wide array of
financial instruments and assets when discussing risk. By defining investment in such
an inclusive manner, we can better understand and analyze the various dimensions of
risk that different types of investments may present.
When we talk about investments, we aren't limiting ourselves to traditional
assets like stocks and bonds. Instead, we are casting a wide net that includes
everything from the balance in a bank account, which is generally considered very
low risk due to the backing of federal insurance programs, to shares of a mutual fund,
which pools money from many investors to purchase a diversified portfolio of stocks,
bonds, or other securities. Mutual funds can vary significantly in terms of risk
depending on their investment strategy, asset allocation, and the specific securities
they hold.
Moreover, our definition extends to more unconventional and often riskier
investments such as lottery tickets, which offer a minuscule chance of a massive
payout in exchange for a very high likelihood of losing the initial investment. While
lottery tickets are typically seen more as a form of gambling than a serious
investment, they do fit within our broad definition because they involve an outlay of
money with the expectation, albeit slim, of a financial return.
Real estate is another important category within our expansive definition of
investment. Real estate investments can range from purchasing a primary residence to
buying rental properties or even investing in real estate investment trusts (REITs).
Each type of real estate investment carries its own unique set of risks, from market
volatility and interest rate changes to property-specific issues such as maintenance
costs and tenant management.
By considering such a wide array of investment types, we can better
appreciate the diverse nature of risks associated with each. For instance, the risk
associated with a bank account balance is primarily related to the financial health of
the banking institution and the extent of deposit insurance coverage. In contrast, the
risks related to mutual funds include market risk, interest rate risk, and credit risk,
among others. Lottery tickets pose a different kind of risk, primarily the risk of loss,
given the extremely low probability of winning. Real estate investments are subject to
market risk, liquidity risk, and operational risks, to name a few.
This broad approach to defining investments and their associated risks allows
us to develop a more comprehensive understanding of risk management strategies.
For example, diversification—spreading investments across various asset classes and
types—can help mitigate risk by reducing the impact of poor performance in any one
investment. Similarly, understanding the specific risks associated with each type of
investment can inform better decision-making and more effective risk mitigation
tactics.
In conclusion, our expansive definition of investment, encompassing
everything from the balance in a bank account to shares of a mutual fund to lottery
tickets and real estate, allows us to thoroughly examine and address the multifaceted
nature of risk in the financial landscape. This holistic perspective is crucial for
developing robust risk management strategies and making informed investment
decisions.
Fifth, risk must be assessed over some time horizon. Every investment has a
time horizon. We hold some investments for a day or two and others for many years.
In most cases, the risk of holding an investment over a short period is smaller than the
risk of holding it over a long one, but there are important exceptions to the rule that
we will discuss later.2 Finally, risk must be assessed relative to a benchmark rather
than in isolation. If someone tells you that an investment is risky, you should
immediately ask: “Relative to what?” The simplest answer is “Relative to an
investment with no risk at all,” called a risk-free investment. But there are other
possibilities, often more appropriate. For example, in considering the performance of
a particular investment advisor or money manager, a good benchmark is the
performance of a group of experienced investment advisors or money managers.
If you want to understand the risk associated with a specific investment
strategy, it is essential to have a point of comparison. The most appropriate
benchmark would be the risk associated with other strategies. This comparative
approach allows investors to gauge the relative riskiness of different strategies and
make more informed decisions based on their risk tolerance, investment goals, and
market conditions.
Investors often face a myriad of choices when selecting an investment
strategy, each with its own unique risk profile. For example, a conservative strategy
might focus on preserving capital and generating steady, albeit lower, returns through
investments in high-quality bonds and dividend-paying stocks. On the other hand, an
aggressive strategy might seek higher returns by investing in small-cap stocks,
emerging markets, or high-yield bonds, which come with greater volatility and risk of
loss. Comparing the risk levels of these strategies helps investors determine which
aligns best with their financial objectives and risk appetite.
Now that we have a foundational understanding of what risk is and how it
varies across different investment strategies, the next logical step is to explore how we
measure this risk. Risk measurement is a critical component of the investment process
because it provides the quantitative basis for assessing potential outcomes and making
informed decisions. By employing various tools and techniques, investors can
estimate the likelihood of different scenarios and their potential impact on their
portfolios.
One of the fundamental tools used in risk measurement is probability theory, a
branch of mathematics that deals with the likelihood of different outcomes.
Probability theory provides a framework for quantifying risk and making predictions
about future events based on historical data and statistical analysis. In the context of
investment, it allows us to estimate the probability of different returns, the likelihood
of achieving specific financial goals, and the potential for losses under various market
conditions.
Probability theory encompasses several key concepts, including expected
value, variance, and standard deviation. The expected value represents the average
outcome of an investment over time, taking into account all possible returns and their
probabilities. Variance measures the dispersion of returns around the expected value,
indicating how much the returns are likely to deviate from the average. Standard
deviation, which is the square root of variance, provides a more intuitive measure of
risk by quantifying the average deviation of returns from the expected value in the
same units as the returns themselves.
In addition to these basic measures, investors use a variety of more
sophisticated tools to assess risk. One common method is Value at Risk (VaR), which
estimates the maximum potential loss of an investment portfolio over a specified time
frame at a given confidence level. VaR provides a single number that summarizes the
risk of a portfolio, making it a valuable tool for risk management and regulatory
compliance. Another important measure is the Sharpe ratio, which adjusts returns for
risk by comparing the excess return of an investment to its standard deviation. A
higher Sharpe ratio indicates a more attractive risk-adjusted return.
Moreover, scenario analysis and stress testing are employed to evaluate how
investment portfolios might perform under different hypothetical conditions. Scenario
analysis involves creating detailed projections based on specific economic or market
events, such as a recession, interest rate changes, or geopolitical crises. Stress testing
goes a step further by examining the impact of extreme, but plausible, adverse events
on the portfolio. These techniques help investors understand the potential
vulnerabilities of their strategies and make necessary adjustments to mitigate risk.
As we delve deeper into the next section, we will explore these rudimentary
tools of probability theory and their application in measuring investment risk. By
understanding these concepts and techniques, investors can gain valuable insights into
the risk profiles of different strategies, make more informed decisions, and develop
robust risk management practices. This knowledge is crucial for navigating the
complexities of the financial markets and achieving long-term investment success.
b. Measuring Risk
Armed with our definition of risk, we are now ready to quantify and measure
it. In this section we will become familiar with the mathematical concepts useful in
thinking about random events. We have already used some of these concepts. Recall
from that the real interest rate equals the nominal interest rate minus expected
inflation. Without the proper tools, we weren’t able to be explicit about what the term
expected inflation means. The same is true of the term expected return. We see now
that the best way to think about expected inflation and expected return is as the
average or best guess—the expected value—of inflation, or the investment’s return
out of all the possible values.
Probability theory tells us that in considering any uncertainty, the first thing
we must do is list all the possible outcomes and then figure out the chance of each one
occurring. When you toss a coin, what are all the possible outcomes? There are two
and only two. The coin can come down either heads or tails. What is the chance of
each one of these two outcomes occurring? If the coin is fair, it will come down heads
half the time and tails the other half; that’s what we mean by fair. If we tossed a fair
coin over and over again, thousands of times, it would come down heads half the time
and tails the other half. But for any individual toss, the coin has an equal chance of
coming down heads or tails. To quantify this statement, we can say that the
probability that the coin will come up heads is one-half.
Probability is a measure of the likelihood that an event will occur. It is always
expressed as a number between zero and one. The closer the probability is to zero, the
less likely it is that an event will occur. If the probability is exactly zero, we are sure
that the event will not happen. The closer the probability is to one, the more likely it is
that an event will occur. If the probability is exactly one, the event will definitely
occur. Some people prefer to think of random outcomes in terms of frequencies rather
than probabilities. Instead of saying that the probability of a coin coming down heads
is one-half, we could say that the coin will come down heads once every two tosses
on average. Probabilities can always be converted into frequencies in this way. To
grasp these concepts, it is helpful to construct a table. The table lists everything=that
can happen (all the possibilities) together with their chances of occurring
(their=probabilities).
In constructing a table like this one, we must be careful to list all possible
outcomes. In the case of a coin toss, we know that the coin can come down only two
ways, heads or tails. We know that one of these outcomes must occur. We just don’t
know which one. One important property of probabilities is that we can compute the
chance that one or the other event will happen by adding the probabilities together. In
the case of the coin flip there are only two possibilities; the probability that the coin
will come up either heads or tails must be one. If the table is constructed correctly,
then, the values in the probabilities column will sum to one. Let’s move from a coin
toss to something a bit more complicated: an investment that can rise or fall in value.
Assume that for $1,000 you can purchase a stock whose value is equally likely to fall
to $700 or rise to $1,400. We’ll refer to the amount you could get back as the
investment’s payoff. Following the procedure we used to analyze the coin toss, we
can construct.
We can now go a step further and compute what is called the expected value of
the investment. We are familiar with the idea of expected value as the average or most
likely outcome. The expected value is also known as the mean. After listing all of the
possible outcomes and the probabilities that they will occur, we compute the expected
value as the sum of their probabilities times their payoffs. (Another way to say this is
that the expected value is the probability-weighted sum of the possible outcomes.)
Computing the expected value of the investment is straightforward.
The expected value of an investment is a very useful concept, but it can be
difficult at first. The problem is that if we make this investment only once, we will
obtain either $700 or $1,400, not $1,050. In fact, regardless of the number of times we
make this particular investment, the payoff will never be $1,050. But what would
happen if we were to make this investment 1 million times? About 500,000 of those
times the investment would pay off $1,400 and the other 500,000 times it would pay
off $700. (Notice that we just converted the probabilities into frequencies.) So the
average payoff from the 1 million investments would be _________ 500,000
1,000,000 ($700) + _________ 500,000 1,000,000 ($1,400) = $1,050 (the expected
value) While the world of casino gambling may offer simple bets with just two
outcomes, the financial world rarely does. To make the example more realistic, let’s
double the number of possibilities and look at a case in which the $1,000 investment
might pay off $100 or $2,000 in addition to $700 or $1,400. We’ll assume that the two
original possibilities are the most likely; the two new possibilities are much less likely
to occur. Note that the probabilities sum to one: 0.1 + 0.4 + 0.4 + 0.1 = 1. Again, we
could convert the probabilities to frequencies, so that 0.4 means 4 out of 10. And
again, we can compute the expected value by multiplying each probability times its
associated payoff and then summing them. So $100 would be the payoff 1 out of
every 10 times, $700 the payoff 4 out of every 10 times, and so on.
Because the expected value of this $1,000 investment is $1,050, the expected
gain is $50. But most people don’t discuss investment payoffs in terms of dollars;
instead, they talk about the percentage return. Expressing the return as a percentage
allows investors to compute the gain or loss on the investment regardless of the size
of the initial investment. In this case, the expected return is $50 on a $1,000
investment, or 5 percent. Note that the two $1,000 investments we just discussed are
not distinguishable by their expected return, which is 5 percent in both cases. Does
that mean an investor would be indifferent between them? Even a casual glance
suggests that the answer is no because the second investment has a wider range of
payoffs than the first. The highest payoff is higher and the lowest payoff lower than
for the first investment. So the two investments carry different levels of risk. The next
section discusses measures of risk. One last word on expected values that to compute
the real interest rate, we need a measure of expected inflation. One way to calculate
expected inflation is to use the technique we just learned. That is, list all the
possibilities for inflation, assign each one a probability, and then calculate the
expected value of inflation.
Most of us have an intuitive sense of risk and its measurement. For example,
we know that walking on a sidewalk is usually a safe activity. But imagine that one
day as you are strolling along, you come upon a 3-foot hole in the sidewalk. The only
way across is to jump over it. If the hole is just a few inches deep, it won’t stop you.
But the deeper it is, the greater the risk of jumping across because the greater the
range of injuries you could sustain. We all have an intuitive sense that the wider the
range of outcomes, the greater the risk. Thinking about risk in terms of the range of
possible outcomes is straightforward. The best way to do it is to start with something
that has no risk at all—a sidewalk without a hole in it or an investment with only one
possible payoff. We will refer to a financial instrument with no risk at all as a risk-free
investment or risk-free asset. A risk-free asset is an investment whose future value is
known with certainty and whose return is the risk-free rate of return. 4 The payoff that
you will receive from such an investment is guaranteed and cannot vary. For instance,
if the risk-free return is 5 percent, a $1,000 risk-free investment will pay $1,050, its
expected value, with certainty. If there is a chance that the payoff will be either more
or less than $1,050, the investment is risky.
Let’s compare this risk-free investment with the first investment we looked at,
the one in which $1,000 had an equal chance of turning into $1,400 or $700. That
investment had the same expected return as the risk-free investment, 5 percent. The
difference is that the payoff wasn’t certain, so risk was involved. What caused the risk
was the increase in the spread of the potential payoffs. The larger the spread, the
higher the risk. These examples suggest that we can measure risk by quantifying the
spread among an investment’s possible outcomes. We will look at two such measures.
The first is based on a statistical concept called the standard deviation and is strictly a
measure of spread. The second, called value at risk, is a measure of the riskiness of
the worst case. When the hole in the sidewalk gets deep enough, you risk being killed
if you fall in.
The standard deviation is more useful than the variance because it is measured
in the same unit as the payoffs: dollars. (Variance is measured in dollars squared.)
That means that we can convert the standard deviation into a percentage of the initial
investment of $1,000, or 35 percent. This calculation provides a baseline against
which we can measure the risk of alternative investments. Given a choice between
two investments with the same expected payoff, most people would choose the one
with the lower standard deviation. A higher-risk investment would be less desirable.
Let’s compare this two-payoff investment with the one that has four possible payoffs.
We already concluded that the second investment is riskier, because the payoffs are
more spread out. But how much riskier is it? To answer this question, we can compute
the standard deviation. That means following the four steps to calculate the variance,
and then taking the square root. This is 1½ times the $350 standard deviation of the
first investment, with only two possible payoffs. Because the two investments have
the same expected value, the vast majority of people would prefer the first. The
greater the standard deviation, the higher the risk.
To see this conclusion graphically, where a $1,000 investment is equally likely
to rise in value to $1,400 or fall in value to $700. That is, there are two possibilities,
each with probability ½: $700 and $1,400. We can plot this on a bar graph, where the
horizontal axis has the payoffs $700 or $1,400 and the height of each bar is the
probability (in this case 0.5 for both). Recall that in this case the $1,000 investment
has four possible payoffs, $100, $700, $1,400 and $2,000, and these occur with
probability 0.1, 0.4, 0.4, and 0.1. As in Case 1, the expected value continues to be
$1,050. Comparing the two figures, we can see that in Case 2, where the investment
has four possible payoffs, the distribution is more spread out. This matches the result
from computing the standard deviation. The more spread out the distribution of
possible payoffs from an investment, the higher the standard deviation and the bigger
the=risk.
Standard deviation is the most common measure of financial risk, and for most
purposes it is adequate. But in some circumstances we need to take a different
approach to the measurement of risk. Sometimes we are less concerned with the
spread of possible outcomes than with the value of the worst outcome. For example,
no one wants the local bank to close its doors. Nor is anyone interested in a discount
price for a life insurance policy from an insurance company that is in poor financial
condition. Neither the customers nor the government regulators care how well or how
badly a financial institution’s shareholders fare, so long as they do well enough to
keep the doors open. The concept used to assess this sort of catastrophic risk is called
value at risk (VaR).
To understand how value at risk works, let’s look at an example. Assume you
are considering buying a house. In going through your finances, you conclude that
you can afford a monthly mortgage payment of $650 and no more. You find a nice
house and a mortgage lender who will lend you $100,000 to buy it. But you need to
decide on the type of mortgage to get. Should it have a fixed or adjustable rate? The
answer is different for different people. But let’s see if we can organize our thinking.
Assume that the current interest rate on a 30-year fixed-rate mortgage (the most
popular kind) is 4 percent, so it has monthly payments around $475, which is within
your budget.5 One alternative is a mortgage with the same 30-year term that adjusts
once a year, starting at 3 percent. The adjustable-rate mortgage has payments that start
at about $420 per month. This looks great. But remember Core Principle 2: Risk
requires compensation. By taking the adjustable-rate mortgage you can save more
than $50 per month. But adjustable rates can adjust, meaning they can go up and
down. That’s a risk. Looking closer, you realize that the mortgage contract specifies
that the adjustments can be as much as 2 percentage points per year, and can go as
high as 11 percent. Which mortgage should you sign up for?
The lower initial monthly payments do seem to come with higher risk.
Without doing any computations, we know that the standard deviation of monthly
payments for a 4 percent fixed-rate mortgage is zero, and that the standard deviation
of the payment for the adjustable-rate mortgage is greater than zero. Let’s just say that
interest rates are not expected to change, so the expected value of the monthly
payments in the second circumstance is just $420. But what does that tell us? The
computation of the expected value and standard deviation does not seem to get at the
heart of the problem. The reason is that it doesn’t take proper account of the worst
case. The interest rate could rise 2 percent per year for the next four years. That means
that your monthly payments could rise to around $535 in the second year after one
adjustment, about $665 in the third year, and go up over $800 in the fourth year.
While you can readily make the $535 payments, more than $650 per month is out of
the question. If interest rates were to rise by 4 percentage points over the next
two=years, you would no longer be able to afford the mortgage payments. That’s
the=risk.
This mortgage example highlights the fact that sometimes risk should be
measured by the value of the worst case rather than be measured by expected value
and standard deviation. Value at risk, which measures risk as the maximum potential
loss, is more appropriate in the example we just studied. VaR is the answer to the
question: How=much will I lose if the worst possible scenario occurs? In the example
of the $1,000 investment, worst case was a loss of $300. In the more complex $1,000
investment, the value at risk was $900—the most you could possibly lose. In the
mortgage example the value at risk is the house: If the payment increases beyond
$650 a month, you can’t make the payments on your loan and you will be forced to
sell the house. There are surely cases where the lower payments of an adjustable-rate
mortgage are worth the risk, but this may not be one of them. A more sophisticated
value-at-risk analysis would include a time horizon and probabilities. In fact, the
formal definition of Value at Risk is the worst possible loss over a specific time
horizon, at a given probability. VaR is a measure of risk that we will find very useful
in discussing the management and regulation of financial institutions. By restricting
the sorts of financial instruments banks can hold, bank managers and financial
regulators try to limit the chances of a financial collapse. Such a collapse is an
example of infrequent but potentially catastrophic events sometimes called tail risks
or black swans (like the enormous 2011 earthquake that produced a tsunami and
nuclear disaster in Japan). To address the dangers associated with financial tail risks,
banks and regulators employ the concept of value at risk.
c. Risk Aversion, the Risk Premium, and the Risk-Return Tradeoff
The implication of our discussion so far is that most people don’t like risk and
will pay to avoid it. While some people enjoy risky activities like skydiving and car
racing, most of us are more careful. And while some people gamble large sums, most
of us don’t because we can’t sustain large losses comfortably. In fact, the reason we
buy insurance is that we want someone else to take the risk. Insurance is an interesting
case; remember, for an insurance company to make a profit, it must charge more than
it expects to pay out. Thus, insurance premiums are higher than the expected value of
the policyholder’s losses. We pay to avoid risks because most of us are risk averse.
To understand risk aversion, imagine that you are offered a single chance to
play a game in which a fair coin will be tossed. If it comes up heads you will win
$1,000; if it comes up tails, you will get nothing. How much would you be willing to
pay to play the game just once? The expected value of the game is $500—that is, on
average, the game yields $500—but you may play only one time. Would you pay
$500 to play the game? If so, you are risk neutral. Most people would not play the
game at $500, though they would at less than that amount. These people are risk
averse. Because the coin toss is similar to an investment, we can apply the same logic
to investor behavior and conclude that a risk-averse investor will always prefer an
investment with a certain return to one with the same expected return but any amount
of uncertainty. (A=risk-neutral person wouldn’t care as long as the expected return is
the same.)
A risk-free investment with a guaranteed return is clearly preferable to a risky
investment with the same expected return but an uncertain outcome. This preference
stems from the inherent desire for security and stability in financial decision-making.
When an investor is faced with the choice between a guaranteed return and a potential
return that carries uncertainty, the psychological comfort of knowing the exact
outcome often outweighs the allure of possibly higher returns that come with risk.
Consider the scenario of a risk-free investment, such as a government bond
that promises a fixed interest rate over a specified period. This type of investment is
backed by the full faith and credit of the issuing government, making it virtually free
of default risk. The guaranteed return provides a sense of security and predictability,
allowing investors to plan their financial future with confidence. This certainty is
especially valuable in times of economic instability or market volatility, where the
predictability of returns becomes a cornerstone of sound financial planning.
In contrast, a risky investment with the same expected return presents a very
different proposition. Here, the expected return is an average outcome that takes into
account all possible scenarios, both positive and negative. While the average might
match the guaranteed return of the risk-free investment, the actual return could vary
significantly. This variability introduces an element of uncertainty and potential for
loss, which many investors find disconcerting. The prospect of experiencing a return
lower than expected, or even a total loss, makes risky investments less appealing
despite the possibility of achieving higher gains.
To illustrate this concept, let’s consider a classic example involving a coin
toss. Suppose you are given a choice between two options: receiving $500 with
certainty or participating in a coin toss where heads results in $1,000 and tails results
in nothing. The expected return of the coin toss can be calculated as follows:
Expected=return=(0.5×$1,000)+(0.5×$0)=$500\text{Expected return} = (0.5 \
times \$1,000) + (0.5 \times \$0) = \
$500Expected=return=(0.5×$1,000)+(0.5×$0)=$500
While the expected return of the coin toss matches the guaranteed $500, most
people would choose the guaranteed $500 over the gamble. This preference is rooted
in risk aversion, a fundamental concept in behavioral economics. Risk aversion
reflects the tendency of individuals to prefer certainty over uncertainty, especially
when the stakes involve significant sums of money or potential losses. The guaranteed
$500 offers a secure and predictable outcome, eliminating the anxiety and stress
associated with the uncertain outcome of the coin toss.
Furthermore, risk aversion can be influenced by various factors, including an
individual's financial situation, investment goals, and personal tolerance for
uncertainty. For someone with limited financial resources or a low tolerance for risk,
the guaranteed return is particularly attractive as it ensures that their financial position
remains stable. On the other hand, a more risk-tolerant investor might be willing to
take on the gamble in pursuit of higher returns, viewing the potential reward as worth
the risk.
In real-world financial markets, this preference for certainty is evident in the
way investors allocate their portfolios. A significant portion of investment capital is
often directed towards low-risk assets such as government bonds, high-quality
corporate bonds, and money market instruments. These investments provide steady,
predictable returns and serve as a foundation of stability within a diversified portfolio.
Riskier assets, such as stocks, commodities, and real estate, are then added to the
portfolio to seek higher returns, but always with an awareness of the potential risks
involved.
Ultimately, the decision between a risk-free investment and a risky one with
the same expected return highlights the importance of understanding one's risk
tolerance and investment objectives. While the allure of potentially higher returns can
be tempting, the comfort and security of a guaranteed return often hold greater appeal,
particularly for those who prioritize financial stability and peace of mind.
In summary, a risk-free investment with a guaranteed return is generally
preferred over a risky investment with the same expected return but uncertain
outcomes. This preference is driven by risk aversion and the desire for predictability
in financial decision-making. The example of the coin toss illustrates this concept
clearly, as most people would choose the certain $500 over the gamble, even though
the expected return is the same. This principle is a cornerstone of prudent investing,
guiding individuals in balancing their pursuit of returns with their tolerance for risk.
One result of this desire to avoid risk is that investors require compensation
for taking risk. That’s the flip side of buying insurance. When we buy insurance, we
pay someone else to take our risks, so it makes sense that if someone wants us to take
on a risk, we need to be paid to do it. A risky investment, then, must have an expected
return that is higher than the return on a risk-free asset. In economic terms, it must
offer a risk premium. In general, the riskier an investment, the higher the risk
premium (the higher the compensation investors require for holding it). By extension,
if riskier investments have higher risk premiums, they must have higher expected
returns.
Thus, there is a fundamental tradeoff between risk and expected return in the
world of investing. This tradeoff is a cornerstone principle in finance, encapsulating
the idea that achieving higher returns generally necessitates taking on higher levels of
risk. This relationship holds true across virtually all types of investments, from stocks
and bonds to real estate and commodities.
When an investor seeks to maximize their returns, they must be willing to
accept the potential for greater variability in those returns. Higher returns are often
accompanied by increased volatility and the potential for significant losses.
Conversely, investments that are perceived as safer typically offer lower returns. This
tradeoff is crucial for investors to understand, as it guides their decisions in
constructing and managing their investment portfolios.
To illustrate this concept, consider different types of investment options. For
example, government bonds are often viewed as some of the safest investments
available. They provide relatively low but stable returns and are backed by the
government, which significantly reduces the risk of default. On the other end of the
spectrum, investing in stocks, particularly those of small-cap or emerging market
companies, can offer the potential for substantial gains. However, these stocks also
come with a higher degree of uncertainty and the risk of significant price fluctuations.
Given this inherent tradeoff, if someone tells you that they have made a big
return on an investment, it is prudent to suspect that the investment involved a high
level of risk. Large returns typically do not materialize without exposure to
considerable risk. For instance, an investor who claims to have doubled their money
in a short period may have invested in highly volatile assets like cryptocurrencies,
penny stocks, or leveraged financial instruments. These investments can indeed yield
impressive returns, but they also come with the possibility of substantial losses.
This principle of "no risk, no reward" is a fundamental aspect of investment
theory. It underscores the idea that there are no free lunches in the financial markets—
achieving higher returns involves taking on higher risk. This risk-return tradeoff is
visually represented in the risk-return spectrum, where different asset classes are
plotted based on their expected returns and associated risks. For example, cash and
cash equivalents, such as savings accounts and Treasury bills, are positioned at the
low-risk, low-return end of the spectrum. In contrast, equities, commodities, and high-
yield bonds occupy the higher-risk, higher-return portion of the spectrum.
Investors must carefully consider their risk tolerance when making investment
decisions. Risk tolerance is influenced by factors such as age, financial goals,
investment horizon, and personal comfort with uncertainty. Younger investors with
longer time horizons might be more willing to take on higher risks in pursuit of
greater returns, as they have more time to recover from potential losses. Conversely,
retirees or those nearing retirement may prioritize capital preservation and opt for
lower-risk investments, even if it means accepting lower returns.
Moreover, understanding the risk-return tradeoff helps investors set realistic
expectations and avoid being swayed by promises of extraordinary returns without
commensurate risk. In financial markets, if something seems too good to be true, it
usually is. Skepticism is a valuable trait, encouraging investors to perform thorough
due diligence and seek a clear understanding of the risks involved in any investment
opportunity.
Risk management also plays a critical role in navigating the risk-return
tradeoff. Diversification, or spreading investments across different asset classes,
sectors, and geographies, can help mitigate risk without sacrificing potential returns.
By not putting all their eggs in one basket, investors can reduce the impact of poor
performance in any single investment.
In conclusion, the tradeoff between risk and expected return is a fundamental
principle in investing. Achieving higher returns generally requires accepting higher
levels of risk. When someone reports substantial returns, it is likely that they have
taken significant risks. This risk-return tradeoff necessitates a careful assessment of
risk tolerance and the implementation of robust risk management strategies.
Ultimately, understanding this relationship is key to making informed investment
decisions and achieving long-term financial goals.
As of the first quarter of 2019, JNJ was in top-notch financial condition, while
JCP was not. That leads us to expect that the return for holding JCP’s bonds would
contain a higher risk premium than would the return for holding JNJ bonds. And it
did. In early 2019, the two companies had bonds with a maturity range of about five
years. Those from JCP paid 25.09 percent, while those from JNJ paid 2.59 percent.
Meanwhile, a five-year U.S. Treasury note paid a meager 2.42 percent. Because the
U.S. Treasury is highly likely to pay, we’ll use 2.42 percent as our estimate of the
risk-free rate. So, to get an estimate of the risk premium for the JNJ and JCP bonds,
we subtract 2.42 from the rate for each: For JCP, the result is 25.09 − 2.42 = 22.67
percent; for JNJ, we get=2.59 − 2.42 = 0.17 percent.
Not surprisingly, the risk premium on the relatively risky company is much
bigger—in this case, more than 100 times bigger! This stark difference highlights the
substantial compensation investors demand for taking on additional risk. The risk
premium represents the extra return that investors require to hold a riskier asset
instead of a risk-free asset. This concept is pivotal in understanding how financial
markets function and why different assets are priced the way they are.
The risk premium can vary significantly based on the perceived riskiness of an
investment. For example, a government bond issued by a stable country with a strong
credit rating might offer a very low risk premium because the likelihood of default is
minimal. In contrast, a corporate bond issued by a company with uncertain financial
prospects or a history of volatility will offer a much higher risk premium to attract
investors. This higher premium compensates for the additional risk of potential
default or financial instability.
Consider a relatively risky company operating in a highly competitive and
unpredictable industry. This company might be a start-up tech firm, an emerging
market enterprise, or a company heavily reliant on volatile commodity prices.
Investors recognize that the future cash flows of such companies are highly uncertain.
They may face significant operational risks, regulatory challenges, or market
competition that can drastically affect their profitability and survival. Consequently,
the risk premium for investing in such a company needs to be substantially higher to
entice investors to take on these risks.
The magnitude of the risk premium can be illustrated with a numerical
example. Suppose the risk-free rate, represented by the yield on government bonds, is
2%. A stable, blue-chip company with a long track record of steady earnings might
have a risk premium of 3%, resulting in a total expected return of 5% for its investors.
On the other hand, a high-risk company with volatile earnings and an uncertain future
might have a risk premium of 300%, leading to a total expected return of 302%. This
difference in risk premiums—3% versus 300%—is enormous, demonstrating how
much more compensation investors require for the higher risk associated with the
second company.
This phenomenon is not just theoretical but can be observed in real-world
market behavior. During periods of economic stability and growth, risk premiums
tend to narrow as investors become more willing to take on risk in search of higher
returns. Conversely, during times of economic uncertainty or financial crises, risk
premiums widen dramatically as investors flee to safety and demand much higher
compensation for holding riskier assets. This dynamic adjustment of risk premiums is
a critical aspect of market cycles and investor sentiment.
Furthermore, the concept of risk premium is closely tied to the Capital Asset
Pricing Model (CAPM), a fundamental model in finance that describes the
relationship between systematic risk and expected return for assets. According to
CAPM, the expected return on an investment is equal to the risk-free rate plus the risk
premium, which is determined by the asset's beta (a measure of its sensitivity to
market movements) and the market risk premium (the excess return expected from the
market portfolio over the risk-free rate).
In the case of the relatively risky company, its high beta would contribute to a
significantly larger risk premium. This high beta reflects the company's high
sensitivity to market fluctuations, indicating that its returns are likely to be more
volatile and more susceptible to broader economic and market trends. Investors
require substantial additional returns to compensate for this higher level of systematic
risk.
The enormous risk premium demanded by investors also underscores the
importance of thorough risk assessment and due diligence. Investors need to carefully
evaluate the specific risks associated with each investment, considering factors such
as industry dynamics, competitive positioning, financial health, management quality,
and macroeconomic conditions. By doing so, they can make more informed decisions
about the appropriate risk premium and whether the potential returns justify the risks.
In conclusion, the risk premium on a relatively risky company is significantly
larger than that of a more stable investment. This substantial difference in risk
premiums reflects the higher compensation investors demand for taking on greater
uncertainty and potential for loss. Understanding the factors that influence risk
premiums and how they adjust in response to market conditions is crucial for
investors aiming to navigate the complex landscape of financial markets and make
sound investment choices.
d. Sources of Risk: Idiosyncratic and Systematic Risk
Risk is everywhere. It comes in many forms and from almost every
imaginable place. In most circumstances the sources of risk are obvious. For drivers,
it’s the risk of an accident; for farmers, the risk of bad weather; for investors, the risk
of fluctuating stock prices. Regardless of the source, however, we can classify all
risks into one of two groups: (1) those affecting a small number of people but no one
else and (2) those affecting everyone. We’ll call the first of these idiosyncratic risks,
or unique risks, and the second systematic risks, or economywide risks.6 To
understand the difference between idiosyncratic and systematic risk, think about the
risks facing Ford Motor Company stockholders. Why should the value of Ford’s stock
go up or down? There are two main reasons. First, there is the risk that Ford will lose
sales to other carmakers. If Ford fares poorly compared with its competition, its
market share (and thus its share of all economic activity) may shrink.
This risk is unique to Ford, because if Ford does relatively poorly, someone
else must be doing relatively better. Idiosyncratic risk, also known as unsystematic
risk, is specific to a single company or a small group of companies. It is the type of
risk that affects individual firms due to factors such as management decisions,
competitive dynamics, product recalls, regulatory changes, or significant shifts in
consumer preferences. This risk contrasts with systematic risk, which affects the
entire market or economy and cannot be easily mitigated through diversification.
Idiosyncratic risk is unique to Ford because the company operates in a highly
competitive and dynamic industry where various players vie for market share. If Ford
faces challenges, such as a decline in vehicle sales, production issues, or unfavorable
changes in trade policies, its competitors might benefit. For example, if Ford struggles
with a significant recall due to a manufacturing defect, consumers might turn to other
automakers like General Motors, Toyota, or Tesla. These companies could potentially
capture the market share lost by Ford, thereby doing relatively better in comparison.
The notion that idiosyncratic risk is specific to individual firms is crucial for
understanding how investors manage and mitigate such risks. Unlike systematic risk,
which is inherent to the entire market and influenced by factors such as economic
recessions, interest rate changes, and geopolitical events, idiosyncratic risk can be
diversified away. By holding a well-diversified portfolio of investments, investors can
reduce the impact of any single company's poor performance on their overall
portfolio. This diversification spreads the risk across various assets, industries, and
geographic regions, minimizing the effect of idiosyncratic risk.
To further illustrate this concept, consider the case of Ford in detail. Ford
operates in the automotive industry, which is subject to various idiosyncratic risks.
These risks might include changes in consumer preferences towards electric vehicles,
the impact of new technologies, such as autonomous driving, or regulatory shifts
aimed at reducing carbon emissions. If Ford fails to adapt to these changes effectively,
it could suffer from declining sales and profitability. Conversely, if a competitor
excels in these areas, it may gain a competitive edge, capturing market share and
improving its financial performance.
Idiosyncratic risk can also arise from internal factors specific to Ford. For
example, management decisions play a critical role in the company's success.
Strategic missteps, such as poorly executed product launches, inefficient cost
management, or failure to innovate, can adversely affect Ford's performance.
Additionally, labor disputes, supply chain disruptions, or adverse publicity can
contribute to the company's unique risks. These factors underline the importance of
robust corporate governance and strategic planning in mitigating idiosyncratic risk.
Investors need to be aware of the idiosyncratic risks associated with individual
companies like Ford when constructing their investment portfolios. Thorough
research and analysis are essential to identify potential risks and opportunities. By
examining a company's financial health, competitive positioning, management
quality, and industry trends, investors can make more informed decisions about the
potential risks and rewards associated with their investments.
One effective way to manage idiosyncratic risk is through diversification. By
holding a mix of assets that are not highly correlated, investors can reduce the overall
volatility of their portfolios. For instance, an investor might diversify their holdings
by including stocks from different sectors, bonds, real estate, and international
investments. This approach ensures that poor performance in one asset or sector does
not disproportionately impact the entire portfolio.
In addition to diversification, investors can use financial instruments such as
options and futures to hedge against specific risks. For example, if an investor is
concerned about potential declines in Ford's stock price due to idiosyncratic risk, they
might purchase put options on Ford's stock. These options would increase in value if
Ford's stock price falls, offsetting some of the losses in the investor's portfolio.
In conclusion, idiosyncratic risk is unique to specific companies like Ford and
arises from factors that affect individual firms rather than the entire market. This type
of risk can be managed and mitigated through diversification and strategic hedging.
Understanding the nature of idiosyncratic risk and how it differs from systematic risk
is crucial for investors looking to build resilient and balanced portfolios. By carefully
analyzing individual companies and incorporating a diverse range of assets, investors
can effectively navigate the complexities of idiosyncratic risk and enhance their long-
term investment success.
The second risk Ford’s stockholders face is that the U.S. industry as a whole
will do poorly. This is systematic, economywide risk. If we think of idiosyncratic risk
as a change in the share of the auto-market pie, systematic risk is a change in the size
of the pie of the entire economy, of which the auto market is a=part. In other words,
systematic risk is the risk that everyone will do poorly at the same time. The entire
economy could slow for reasons that are completely unrelated to any individual
company’s performance. Macroeconomic factors, such as swings in consumer and
business confidence brought on by global economic conditions or changes in the
political climate, are the source of systematic risks that affect all firms and individuals
in the entire economy. Idiosyncratic risks come in two types. In the first, one set of
firms is affected in one way and other firms in another way.
An example would be a change in the price of oil. History tells us that when
oil prices rise, auto sales fall, and the automobile industry suffers. But higher oil
prices improve the profits of firms that supply energy, such as ExxonMobil, Shell, and
Texaco. An oil price change that is bad for Ford is good for the oil companies.
Looking at the economy as a whole, this is an idiosyncratic risk. Not all idiosyncratic
risks are balanced by opposing risks to other firms or industries. Some unique risks
are specific to one person or company and no one else.
The risk that two people have an automobile accident is unrelated to whether
anyone else has one. This type of risk is an example of what we call idiosyncratic or
unsystematic risk. These risks are specific to individual events, entities, or situations
and do not have a broader impact on the overall market or economic system. In the
context of our example, each car accident is an independent event, meaning that the
occurrence of one accident does not influence the likelihood of another. Because these
risks are isolated and affect only specific individuals or entities, they fall under the
category of idiosyncratic risks.
Idiosyncratic risks are pervasive in various aspects of life and business,
reflecting the unique uncertainties faced by individuals or single entities. These risks
are distinct from systematic risks, which affect entire markets or economic sectors and
cannot be mitigated through diversification. While systematic risks arise from
macroeconomic factors such as inflation, interest rates, or geopolitical events,
idiosyncratic risks are tied to specific situations and can often be managed or reduced
through careful planning and diversification.
Consider the broader context of idiosyncratic risks within different industries
and everyday scenarios. In the automotive industry, for example, an individual’s
likelihood of experiencing a car accident depends on numerous personal factors, such
as driving behavior, vehicle maintenance, road conditions, and adherence to traffic
laws. These factors are unique to each driver and do not correlate with the experiences
of other drivers. Consequently, the risk of an accident for one driver remains
independent of the risk faced by another.
Similarly, in the realm of business, companies face various idiosyncratic risks
based on their specific circumstances. A manufacturing firm might encounter risks
related to machinery breakdowns, supply chain disruptions, or labor strikes. These
events are specific to the firm and do not necessarily impact other companies in the
same industry. For instance, if a manufacturing plant experiences a machinery failure,
it might face production delays and increased costs, but this incident does not affect
the operations of another plant using different machinery.
Financial markets provide another illustration of idiosyncratic risks. When
investing in individual stocks, investors must consider the unique risks associated
with each company. These risks can include factors such as management decisions,
product recalls, regulatory changes, or competitive pressures. For example, if a
pharmaceutical company faces regulatory hurdles in obtaining approval for a new
drug, its stock might suffer. However, this specific risk does not influence other
pharmaceutical companies that do not face the same regulatory challenges.
Idiosyncratic risks are not confined to negative outcomes; they can also
include positive developments unique to an individual or entity. For example, a
technology startup might experience a breakthrough in developing a new product,
leading to substantial growth and profitability. This positive idiosyncratic event
benefits the startup but does not directly affect other companies in the technology
sector.
One of the key strategies for managing idiosyncratic risk is diversification. By
spreading investments across a range of assets, sectors, and geographic regions,
investors can reduce the impact of any single event on their overall portfolio. For
instance, an investor who diversifies their holdings among different stocks, bonds,
real estate, and international assets is less likely to experience significant losses due to
idiosyncratic risks affecting one particular investment. Diversification helps to smooth
out the volatility associated with specific risks, leading to a more stable and resilient
portfolio.
In addition to diversification, risk management techniques such as hedging can
also mitigate idiosyncratic risks. For example, a farmer concerned about the risk of
crop failure due to weather conditions might use futures contracts to lock in prices for
their produce, thus reducing the financial impact of adverse weather events. Similarly,
a company exposed to currency risk due to international operations might use
currency hedging to protect against unfavorable exchange rate fluctuations.
Understanding the distinction between idiosyncratic and systematic risks is
crucial for effective risk management. While idiosyncratic risks can often be
mitigated through diversification and targeted strategies, systematic risks require
broader measures such as asset allocation, macroeconomic analysis, and strategic
planning to address their potential impact.
In conclusion, idiosyncratic risks are unique to individual events, entities, or
situations and are independent of broader market or economic trends. These risks,
such as the likelihood of two people having unrelated car accidents, highlight the
importance of diversification and specific risk management strategies in mitigating
their impact. By recognizing and addressing idiosyncratic risks, individuals and
businesses can enhance their resilience and improve their ability to navigate
uncertainties in various aspects of life and commerce.
e. Reducing Risk through Diversification
When George T. Shaheen left his $4 million-a-year job overseeing 65,000
employees of a large management consulting firm to become chief executive of the
Webvan Group, he may not have realized how much of a risk he was taking. He
thought Webvan would change the way people bought their groceries. Consumers
would order their cereal, milk, apples, and ice cream over the Internet, and Webvan
would deliver to their door. In November 1999, just a few months after Shaheen
joined the company, his stock in Webvan was worth more than $280=million. But by
April 2001, his shares were worth a paltry $150,000 and Shaheen had left the
company. On July 10, 2001, Webvan collapsed and stockholders were left with
nothing.
What happened to Webvan and its plan to change the way people shop?
Maybe people actually like getting out of the house and going to the grocery store. Or
maybe Webvan was just ahead of its time. But this story is about more than shopping;
it’s also about risk. Shaheen took on so much risk that a single big loss wiped him out.
Traders in the financial markets call this experience “blowing up.” Surely Shaheen
could have done something to protect at least a portion of his phenomenal wealth
from the risk that it would suddenly disappear. But what? Cervantes answered this
question in Don Quixote in 1605: “It is the part of a wise man to keep himself today
for tomorrow, and not to venture all his eggs in one basket.” In today’s terminology,
risk can be reduced through diversification, the principle of holding more than one
risk at a time. Though it may seem counterintuitive, holding several different
investments can reduce the idiosyncratic risk an investor bears. A=combination of
risky investments is often less risky than any one individual investment. There are two
ways to diversify your investments. You can hedge risks or you can spread them
among the many investments. Let’s discuss hedging first.
Hedging is the strategy of reducing idiosyncratic risk by making two
investments with opposing risks. When one does poorly, the other does well, and vice
versa. So while the payoff from each investment is volatile, together their payoffs are
stable. Consider the risk an investor faces from a potential change in the price of oil.
Increases in the price of oil are bad for most of the economy, but they are good for oil
companies. So an investor might buy stock in both 3M, maker of a wide range of
products for consumer, medical and industrial uses; and Texaco, a large oil company.
For the sake of our example, let’s assume that oil prices have an equal chance of
rising or falling. When they rise, owners of Texaco stock receive a payoff of $120 for
each $100 they invested. When oil prices fall, Texaco’s shareholders just get their
$100 investment back. The reverse is true for 3M. When oil prices fall, owners of 3M
stock get $120 for each $100 they invested; when oil prices rise, they get $100.
But what about the third option? What if you split your $100 and put half in
3M and half in Texaco? Because $50 is half the size of your initial investment, the
payoff is half as big as well—a $50 investment in either stock pays off either $60=or
$50. But the important point about this strategy is that it reduces your risk. When oil
prices go up, Texaco does well but 3M does badly. When oil prices fall, the reverse
happens. Regardless of whether oil prices go up or down, you will get back $110 on
your $100 investment. Investing $50 in each stock ensures your payoff. Hedging—
splitting your investment between two stocks with different payoff patterns—has
eliminated your risk entirely. Could George Shaheen have hedged the risk of=owning
so much Webvan stock? To do it, he would have had to find a company whose stock
price would rise when Webvan’s fell. That would have been=difficult, because
Webvan’s business concept= was new= and untested. But Shaheen did have another
option.
lways reduce risk through hedging. Fortunately, there is another way. You can
simply spread risk around—and that’s what George Shaheen should have done. To
spread your risk, all you need to do is find investments whose payoffs are unrelated.
Let’s replace Texaco with Microsoft and assume that 3M and Microsoft’s payoffs are
independent of each other.7 So we toss a coin once to see if 3M does well or badly,
and then we toss it a second time to see how Microsoft does. As before, a $100
investment in either company pays off either $120 or $100 with equal probability.
Again, we’ll consider three investment strategies: (1) 3M only, (2) Microsoft only,
and (3) half in 3M and half in Microsoft. The expected payoff on each of these
strategies is the same: $110. For the first two strategies, $100 in either company, the
standard deviation is still $10, just as it was before. But for the third strategy, $50 in
3M and $50 in Microsoft, the analysis is more complicated. There are four possible
outcomes, two for each stock.
