FNCE 625 – Investment Analysis and Management

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Investments: Analysis and Management

Fourteenth Edition

Gerald R. Jensen and Charles P. Jones

Chapter 17

Bond Yields and Prices

Interest Rate

Rental rate for loanable funds

Basis point

100 basis points equals one percentage point

Riskless rate is foundation for other rates

Approximated by rate on Treasury securities

Other rates differ because of

Maturity differentials

Security risk premiums

Interest Rates 1

Opportunity cost of foregoing consumption

Real risk-free rate (real rate) unaffected by price changes or risk factors

Nominal (observed) risk-free rate (R F) includes a real component (r r) and expected inflation (e i)

Interest Rates 2

All interest rates are described according to the following formula

Where rp incorporates all risk premiums associated with features such as time to maturity, liquidity, credit quality, etc.

Term Structure of Interest Rates 1

Relationship between time to maturity and yield to maturity (yield curve)

Yield curves

Graphical depiction of the relationship between yields and time to maturity

Default risk held constant

Observations involve tendencies rather than exact relationships

Term Structure of Interest Rates 2

Upward-sloping yield curve

Typical, interest rates rise with maturity

Downward-sloping yield curves

Unusual, predictor of recession?

Term structure theories

Explanations of the shape of the yield curve

Pure expectations, liquidity preference, and preferred habitat

Forward Rates

Forward rates are unobservable rates expected to prevail in the future

Are not observable, but are commonly estimated from longer-term bond rates

For example, the rate on a 3-yr bond can be decomposed into the current 1-yr rate and 2 1-yr forward rates

Pure Expectations Theory

Long-term rates are an average of current and expected future short-term rates

No other considerations matter

According to the theory, forward rates derived from current longer-term rates equal expected future rates

Theory is not that forward rates will be correct, but that there is a relationship between them and current rates

What does the Yield Curve tell us?

Slope of the Yield Curve:

upward - investors expect interest rates to increase

downward - investors expect interest rates to drop

flat - investors expect interest rates to remain constant

Liquidity Preference Theory

Rates reflect current and expected short rates, plus liquidity risk premiums

Uncertainty increases with time

Investors prefer to lend for short run, borrowers to borrow for long run

Liquidity premium is required to induce long-term lending

Derived forward rates do not equal expected future rates

Preferred Habitat Theory

Market participants have preferred maturity segments

Must be induced to move out of their preferred segment

Market segmentation theory is a more extreme version

Interest rates are determined by supply and demand in each segment

Yield Spreads

Risk premiums

Result from differences in

Default risk (bond rating), maturity, call features, coupon rates, marketability, taxes

Borrower actions

Interest rates

Function of variables associated with issue or issuer

Inversely related to business cycle

Credit Spread/Default Premium

Bond Ratings - S&P/Moody’s

AAA	Aaa	Highest Quality
AA	Aa	High Quality
A	A	Upper Medium Grade
BBB	Baa	Medium Grade
BB	Ba	Speculative Elements
B	B	Speculative
CCC	Caa	Poor Standing
CC	Ca	Highly Speculative
CD	C	Extremely Poor Prospects of ever attaining investment standing

Measuring Bond Yields 1

Premium: price > par value

Discount: price < par value

Interest payments (coupons) on bonds usually paid semi-annually

Current yield: ratio of coupon interest to current market price

Does not account for difference between purchase price and redemption value

Measuring Bond Yields 2

Yield to maturity (Y T M)

Most commonly used measure of bond return

Promised return received from a bond purchased at the current market price

If held to maturity

And coupons reinvested at Y T M

Likelihood of meeting second condition is extremely small

Yield to Maturity 1

Solve for Y T M:

For a zero coupon bond the first term in the equation does not exist.

Yield to Maturity 2

Some bonds are callable after deferred call period

Y T M unrealistic for bonds likely to be called

Often uses end of deferred call period

Substitute number of periods until first call for date and call price (C P) for face value

Realized Compound Yield (R C Y)

Rate of return actually earned on a bond given the reinvestment of coupons at varying rates

Determined after investment concluded

Rarely equal to Y T M

Reinvestment Risk 1

Interest-on-interest

Reinvestment rate risk

Risk that future reinvestment rates will be less than the Y T M when bond is purchased

Total dollar return on a bond consists of

Coupons paid

Capital gains or losses

Interest income from reinvestment of coupons

Reinvestment Risk 2

Reinvestment increase in importance as coupon or time to maturity (or both) increase

For long-term bonds, interest-on-interest can be most important part of total return

Zero-coupon bonds eliminate reinvestment rate risk

Horizon return analysis

Bond returns based on assumptions about reinvestment rates and yield-to-maturity at end of investment horizon

Bond Valuation Principle

Intrinsic value

An estimated value

Present value of the expected cash flows

Required to compute intrinsic value

Expected cash flows

Timing of expected cash flows

Discount rate, or required rate of return by investors

Bond Valuation

Value of a coupon bond:

Biggest problem is determining the discount rate or required yield (r)

Required yield is the current market rate earned on comparable bonds with same maturity and credit risk

Bond Price Changes 1

Over time, bond prices move toward face

On bond’s maturity date, it must be worth its face value

Bond prices move inversely to market yields

Long-term bond prices fluctuate more than short-term

The change in bond prices due to a yield change is directly related to time to maturity and inversely related to coupon rate

Bond Price Changes 2

Bond Price Relative to Yield

Holding maturity constant, a rate decrease raises prices more than the same increase in rates lowers prices

Yield Change

Decrease from 8% to 6%

Price rises by $231.15

Increase from 8% to 10%

Price drops by $171.59

Implications for Investors

If anticipating a rate decrease, bond buyers should purchase low-coupon, long-maturity bonds

If interest rates are expected to increase, investors should consider bonds with large coupons or short maturities or both

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FNCE 625 – Investment Analysis and Management

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