Financial News Discussion
BabyTazz21
CF5e_PPT_Ch06-Part1.pptx1
Ehrhardt & Brigham
Corporate Finance:
A Focused Approach 5e
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CHAPTER 6
Risk and Return
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Topics in Chapter
Basic return and risk concepts
Stand-alone risk
Portfolio (market) risk
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Value = + + +
FCF1
FCF2
FCF∞
(1 + WACC)1
(1 + WACC)∞
(1 + WACC)2
Free cash flow
(FCF)
Market interest rates
Firm’s business risk
Market risk aversion
Firm’s debt/equity mix
Cost of debt
Cost of equity
Weighted average
cost of capital
(WACC)
Net operating
profit after taxes
Required investments
in operating capital
−
=
Determinants of Intrinsic Value:
The Cost of Equity
...
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What are investment returns?
Investment returns measure the financial results of an investment.
Returns may be historical or prospective (anticipated).
Returns can be expressed in:
Dollar terms.
Percentage terms.
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An investment costs $1,000 and is sold after 1 year for $1,060. See excel.
Dollar return:
Percentage return:
$ Received - $ Invested
$1,060 - $1,000 = $60.
$ Return/$ Invested
$60/$1,000 = 0.06 = 6%.
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What is investment risk?
Investment risk is exposure to the chance of earning less than expected.
The greater the chance of a return far below the expected return, the greater the risk.
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Scenarios and Returns for the 10-Year Zero Coupon T-bond Over the Next Year See excel.
| Scenario | Probability | Return |
| Worst Case | 0.10 | −14% |
| Poor Case | 0.20 | −4% |
| Most Likely | 0.40 | 6% |
| Good Case | 0.20 | 16% |
| Best Case | 0.10 | 26% |
| 1.00 |
Discrete Probability Distribution for Scenarios
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Series 1 -0.14000000000000001 -4.0000000000000036E-2 6.0000000000000039E-2 0.16000000000000009 0.26 0.1 0.2 0.4 0.2 0.1
Returns
Probability
Example of a Continuous Probability Distribution
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Y-Values -0.24000000000000016 -0.1971428571428572 -0.1542857142857143 -0.1114285714285715 -6.8571428571428561E-2 -2.5714285714285731E-2 1.7142857142857154E-2 6.0000000000000032E-2 0.10285714285714286 0.14571428571428588 0.18857142857142881 0.23142857142857137 0.2742857142857143 0.31714285714285761 0.36000000000000026 2.6704962625336052E-3 6.5375840256183884E-3 1.7683964143047161E-2 3.9915156837658936E-2 7.5181184606597784E-2 0.11817001437822749 0.15500372857421424 0.16967574234420477 0.15500372857421421 0.11817001437822762 7.5181184606597729E-2 3.9915156837659005E-2 1.7683964143047081E-2 6.537584025618437E-3 2.6704962625335757E-3
Returns
= 0.10(-14%) + 0.20(-4%) + 0.40(6%)
+ 0.20(16%) + 0.10(26%)
= 6%
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10-Year Zero Coupon T-bond Over the Next Year See Excel
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Data calculated in Excel
| Calculating Expected Returns | |||
| Inputs: | Expected Return | ||
| Scenario | Probability of Scenario (1) | Rate of Return (2) | Product of Probability and Return (1) x (2) = (3) |
| Worst Case | 0.10 | −14% | −1.4% |
| Poor Case | 0.20 | −4% | −0.8% |
| Most Likely | 0.40 | 6% | 2.4% |
| Good Case | 0.20 | 16% | 3.2% |
| Best Case | 0.10 | 26% | 2.6% |
| 1.00 | Exp. ret. = | Sum = 6.0% |
Stand-Alone Risk: Standard Deviation
Stand-alone risk is the risk of each asset held by itself.
Standard deviation measures the dispersion of possible outcomes.
For a single asset:
Stand-alone risk = Standard deviation
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σ2 = 0.10 (-0.14 – 0.06)2
+ 0.20 (-0.04 – 0.06)2
+ 0.40 ( 0.06 – 0.06)2
+ 0.20 ( 0.16 – 0.06)2
+ 0.10 ( 0.26 – 0.06)2
σ2 = 0.0120
σ =
σ = 0.1095 = 10.95%
Standard Deviation of the Bond’s Return During the Next Year See Excel
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Understanding the Standard Deviation
If the returns are normally distributed:
Outcome will be more than 1 σ away from about 31.74% ≈ 32% of the time:
16% of the time below −σ
16% of the time above +σ.
If = 6% and σ =10.95% ≈ 11%:
16% of the time return <−5% = 6% − 11%
16% of the time return > 17% = 6% + 11
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Useful in Comparing Investments
Investments with bigger standard deviations have more risk.
High risk doesn’t mean you should reject the investment, but:
You should know the risk before investing
You should expect a higher return as compensation for bearing the risk.
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Using Historical Data to Estimate Risk
Analysts often use discrete outcomes to analyze risk for projects.
But for investments, most analysts normally use historical data rather than discrete forecasts to estimate an investment’s risk unless it is a very special situation.
Most analysts use:
48 to 60 months of monthly data, or
52 weeks of weekly data, or
Shorter period using daily data.
Use annual returns here for sake of simplicity.
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Historical Data for Stock Returns See Excel
| Year | Market | Blandy | Gourmange |
| 1 | 30% | 26% | 47% |
| 2 | 7 | 15 | −54 |
| 3 | 18 | −14 | 15 |
| 4 | −22 | −15 | 7 |
| 5 | −14 | 2 | −28 |
| 6 | 10 | −18 | 40 |
| 7 | 26 | 42 | 17 |
| 8 | −10 | 30 | −23 |
| 9 | −3 | −32 | −4 |
| 10 | 38 | 28 | 75 |
Average and Standard Deviations for Stand-Alone Investments
Use formulas shown previously (tedious) or use Excel (easy)
What is Blandy’s stand-alone risk?
Note: analysts often use past risk as a predictor of future risk, but past returns are not a good prediction of future returns.
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| Market | Blandy | Gourmange | |
| Average return | 8.0% | 6.4% | 9.2% |
| Standard deviation | 20.1% | 25.2% | 38.6% |
How risky is Blandy stock?
Assumptions:
Returns are normally distributed, so about 16% of the time, return will be less than the average minus σ; about 16% of the time the return will be greater than the average plus σ.
σ is 25.2%
Expected return is about 6.4%.
About 16% of the time, return will be:
< −18.8% (6.4%−25.2% = −18.8%)
> 31.6% (6.4%+25.2% = 31.6%)
Stocks are very risky!
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Portfolio Returns
The percentage of a portfolio’s value that is invested in Stock i is denoted by the “weight” wi. Notice that the sum of all the weights must equal 1.
With n stocks in the portfolio, its return each year will be:
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Example: 2-Stock Portfolio
Form a portfolio by selling 25% of the Blandy stock and investing it in the higher-risk Gourmange stock.
The portfolio return each year will be:
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Historical Data for Stocks and Portfolio Returns
| Year | Blandy | Gourmange | Portfolio of Blandy and Gourmange |
| 1 | 26% | 47% | 31.3% |
| 2 | 15 | −54 | −2.3 |
| 3 | −14 | 15 | −6.8 |
| 4 | −15 | 7 | −9.5 |
| 5 | 2 | −28 | −5.5 |
| 6 | −18 | 40 | −3.5 |
| 7 | 42 | 17 | 35.8 |
| 8 | 30 | −23 | 16.8 |
| 9 | −32 | −4 | −25.0 |
| 10 | 28 | 75 | 39.8 |
Portfolio Historical Average and Standard Deviation
The portfolio’s average return is the weighted average of the stocks’ average returns.
The portfolio’s standard deviation is less than either stock’s σ!
What explains this?
See Excel
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| Blandy | Gourmange | Portfolio | |
| Average return | 6.4% | 9.2% | 7.1% |
| Standard deviation | 25.2% | 38.6% | 22.2% |
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Adding Stocks to a Portfolio
What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?
sp would decrease because the added stocks would not be perfectly correlated.
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Risk vs. Number of Stocks in Portfolio
10 20 30 40 2,000 stocks
Company Specific (Diversifiable) Risk
Market Risk
20%
0
Total Portfolio Risk, p
p
35%
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Reality and Diversification
A portfolio can contain more than stock. Finance textbooks focus only on stocks – not good.
You can diversify your investments by investing in:
Real Estate
Precious metals (Gold and Silver)
Invest in privately held businesses – or start your own business
Art
Toys, comic books and baseball cards?? Yes.
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A Toy Example
In in the 1980’s I was 15 and owned a Baseball Card and Comic Shop and I also sold toy figures
My father taught me how to invest. So what did I do?
I bought a GI Joe figure in 1985 and kept it sealed
I paid $0.99 for the GI Joe Toy in 1985.
I sold the Toy in 2012 for $1,200
What is my annual return on my investment?
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A Toy Example – The Return on Investment
I paid .99 cents for the Toy in 1985: PV = -.99
I sold it for $1,200 in 2012: FV = 1,200
I held the investment from 1985 to 2012: N = 2012 – 1985 = 27
What was my annual return on investment? CPT I/Y
PV = -.99 (it negative because I paid for it)
FV = 1,200 (it is positive because I was paid this amount)
N = 27 (I held the investment for 27 years)
CPT I/Y = 30.07 percent per year on my investment.
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Conclusions
As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.
sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20% = sM .
By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.
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