Bond Yields and Prices Chapter 17 Charles P. Jones, Investments: Analysis and Management, Twelfth Edition, John Wiley & Sons

Interest Rates Price for loanable funds Rates and basis points 100 basis points are equal to one percentage point Short-term riskless rate foundation for other rates Approximated by rate on Treasury bills Other rates differ because of Maturity differentials Security risk premiums

Opportunity cost of foregoing consumption Real risk-free rate of interest (real rate) unaffected by price changes or risk factors Nominal (current) interest rates consist of real rate (rr) + adjustment for expected inflation (ei) IR = rr + ei + rp Equation for all interest rates Rp = all risk premiums, including time and credit quality 17-3 3

The Term Structure of Interest Rates Relationship between time to maturity and yields Yield curves Graphical depiction of the relationship between yields and time for bonds of same issuer Default risk held constant Observations involve tendencies rather than exact relationships 18-4

Term Structure of Interest Rates 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 and why it changes shape over time 18-5

Pure Expectations Theory Long-term rates are an average of current short-term rates and those expected to prevail over the long-term period (“forward rates”) Average is geometric rather than arithmetic Forward rates cannot be easily measured but can be inferred Theory is not that forward rates will be correct but that there is a relationship between them and current rates 18-6

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 to induce long-term lending Interest rate expectations are uncertain 18-7

Yield Spreads Risk premiums Result from Different default risks, maturities, call features, coupon rates, marketability, taxes Borrower actions Interest rates Function of variables associated with issue or issuer Inversely related to business cycle

Measuring Bond Yields 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

Yield to maturity (YTM) Most commonly used Promised compound rate of return received from a bond purchased at the current market price If held to maturity And coupons reinvested at same YTM Likelihood of meeting second condition is extremely small 17-10

Yield to Maturity Solve for YTM: For a zero coupon bond

Yield to First Call Some bonds callable after deferred call period YTM unrealistic for bonds likely to be called Often uses end of deferred call period Substitute number of periods until first call date for and call price for face value

Realized Compound Yield Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates Determined after investment concluded Rarely equal to YTM

Reinvestment Risk Interest-on-interest Reinvestment rate risk Risk that future reinvestment rates will be less than the YTM when bond is purchased Total dollar return on a bond consists of Coupons paid Capital gains or losses Interest income from reinvestment of coupons 17-14

Reinvestment Risk Reinvestment increase in importance as coupon or time to maturity (or both) increases 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 17-15

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

Bond Price Changes Over time, bond prices that differ from face value must change 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 indirectly related to coupon rate

Bond prices $1000 30 25 20 15 10 5 1 Passage of time 17-19

Bond Price Changes Holding maturity constant, a rate decrease will raise prices a greater percent than a corresponding increase in rates will lower prices Price Market yield

Implications for Investors Bond buyers should purchase low-coupon, long-maturity bonds If interest rates expected to increase, investor should consider bonds with large coupons or short maturities or both 17-21

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