MGMT 377

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MGMT 377
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Yield Measures

• NY Nominal Yield (Coupon Rate)
• CY Current Yield (income rate)
• YTMYield to maturity
• YTCYield to call
• RCYRealized compound yield.
• Price Changes

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Yield to Maturity

• Solve for YTM
• For a zero coupon bond
• Investors earn the YTM if the bond is held to
  maturity and all coupons are reinvested at YTM

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Yield to Call

• Yield to a specified call date and call price
• Substitute number of periods until first call
  date for and call price for face value

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Realized Compound Yield

• Rate of return actually earned on a bond given
  the reinvestment of the coupons at varying rates
• Can only be calculated after investment period is
  over
• Horizon return analysis
• Bond returns based on assumptions about
  reinvestment rates

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RIR YTM
RIR gt YTM
RIR lt YTM
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Bond Price Changes

• What happens to FMV when interest rates change?

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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
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Measuring Bond Price Volatility Duration

• Important considerations
• Different effects of yield changes on the prices
  and rates of return for different bonds
• Maturity inadequate measure of a bonds economic
  lifetime
• A measure is needed that accounts for both size
  and timing of cash flows

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Sensitivity to Rate Changes

• Maturity differences.

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Whats the only difference between the two bond?
Bond 2 is more volatile.
Bond 2 maturity gt Bond 1 maturity
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Sensitivity to Rate Changes

• Coupon Rate Differences.

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Whats the only difference between the two bond?
Bond 1 is more volatile.
Bond 2 Coupon gt Bond 1 Coupon
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Summary of Volatility to Rate Changes

• Greater Maturity, Greater Volatility to rate
  changes.
• Lower Coupon, Greater Volatility to rate Changes.

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Duration

• A measure of a bonds lifetime, stated in years,
  that accounts for the entire pattern (both size
  and timing) of the cash flows over the life of
  the bond
• The weighted average maturity of a bonds cash
  flows
• Weights determined by present value of cash flows

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Calculating Duration

• Need to time-weight present value of cash flows
  from bond
• Duration depends on three factors
• Maturity of the bond
• Coupon payments
• Yield to maturity

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Duration Used to Estimate Volatility

• Higher the duration, the greater the volatility
  of the bond to rate changes
• Need to calculate a Modified duration to estimate
  the volatility.

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Estimating Price Changes Using Duration

• Modified duration DD/(1r/2)
• Dcan be used to calculate the bonds percentage
  price change for a given change in interest rates

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Duration Relationships

• Duration increases with time to maturity but at a
  decreasing rate
• For coupon paying bonds, duration is always less
  than maturity
• For zero coupon-bonds, duration equals time to
  maturity
• Duration increases with lower coupons.
• Duration increases with lower yield to maturity.

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Why is Duration Important?

• Allows comparison of effective lives of bonds
  that differ in maturity, coupon
• Used in bond management strategies particularly
  immunization
• Measures bond price sensitivity to interest rate
  movements, which is very important in any bond
  analysis

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Convexity

• Refers to the degree to which duration changes as
  the yield to maturity changes
• Price-yield relationship is convex
• Duration equation assumes a linear relationship
  between price and yield
• Convexity largest for low coupon, long-maturity
  bonds, and low yield to maturity

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Duration Conclusions

• To obtain maximum price volatility, investors
  should choose bonds with the longest duration
• Duration is additive
• Portfolio duration is just a weighted average
• Duration measures volatility which isnt the only
  aspect of risk in bonds

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Bond Investment Strategies
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Risk Structure of Rates

• Yield spreads
• Relationship between yields and the particular
  features on various bonds

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Bond Yield Spread

• Attributes that affect a bonds value
• Time to maturity
• Term structure
• Coupon rate
• Call provisions
• Tax status
• Marketability
• Default probability

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Term Structure of Interest Ratesand Yield Curves

• Term Structure of Interest Rates relationship
  between the interest rate or rate of return
  (yield) on a bond and its time to maturity.
• Yield Curve a graph that represents the
  relationship between a bonds term to maturity
  and its yield at a given point in time.

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Figure 10.3 Two Types of Yield Curves
Most common form
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Theories on Shape of Yield Curve

• Slope of yield curve affect by
• Inflation expectations
• Liquidity preferences of investors
• Supply and demand

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Theories on Shape of Yield Curve

• Expectations Hypothesis
• Shape of yield curve is based upon investor
  expectations of future behavior of interest rates
• If expect higher inflation, investors demand
  higher interest rates on longer maturities to
  compensate for risk
• Increasing inflation expectations will result in
  upward-sloping yield curve
• Decreasing inflation expectations will result in
  downward-sloping yield curve

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Theories on Shape of Yield Curve

• Liquidity Preference Theory
• Shape of yield curve is based upon the length of
  term, or maturity, of bonds
• If investors money is tied up for longer periods
  of time, they have less liquidity and demand
  higher interest rates to compensate for real or
  perceived risks
• Investors wont tie their money up for longer
  periods unless paid more to do so

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Theories on Shape of Yield Curve

• Market Segmentation Theory
• Shape of yield curve is based upon the supply and
  demand for funds
• The supply and demand changes based upon the
  maturity levels short-term vs. long-term
• If more borrowers (demand) want to borrow
  long- term than investors want to invest (supply)
  long-term, then the interest rates (price) for
  long-term funds will go up
• If fewer borrowers (demand) want to borrow
  long- term than investors want to invest (supply)
  long-term, then the interest rates (price) for
  long-term funds will go down

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Interpreting Shape of Yield Curve

• Upward-sloping yield curves result from
• Higher inflation expectations
• Lender preference for shorter-maturity loans
• Greater supply of shorter-term loans
• Flat or downward-sloping yield curves result
  from
• Lower inflation expectations
• Lender preference for longer-maturity loans
• Greater supply of longer-term loans

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• Yield Curve

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Basic Bond Investing Strategy

• If you expect interest rates to increase, buy
  short-term bonds.
• If you expect interest rates to decrease, buy
  long-term non-callable bonds.

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Passive Bond Strategies

• Investors do not actively seek out trading
  possibilities in an attempt to outperform the
  market
• Bond prices fairly determined
• Risk is the portfolio variable to control
• Investors do assess default and call risk
• Diversify bond holdings to match preferences

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Passive Bond Strategies

• Buy and hold
• Choose most promising bonds that meet the
  investors requirements
• No attempt to trade in search of higher returns
• Indexing
• Attempt to match performance of a well known bond
  index
• Indexed bond mutual funds

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Immunization

• Used to protect a bond portfolio against interest
  rate risk
• Price risk and reinvestment risk cancel
• Price risk results from relationship between bond
  prices and rates
• Reinvestment risk results from uncertainty about
  the reinvestment rate for future coupon income

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Immunization

• Risk components move in opposite directions
• Favorable results on one side can be used to
  offset unfavorable results on the other
• Portfolio immunized if the duration of the
  portfolio is equal to investment horizon
• Like owning zero-coupon bond

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Active Bond Strategies

• Requires a forecast of changes in interest rates
• Lengthen (shorten) maturity of bond portfolio
  when interest rates are expected to decline
  (rise)
• Horizon analysis
• Projection of bond performance over investment
  horizon given reinvestment rates and future yield
  assumptions

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Active Bond Strategies

• Identify mispricing among bonds then swap
• Substitution swap, yield pickup swap, rate
  anticipation swap, sector swap
• Interest rate swaps
• Exchange a series of cash flows
• Convert from fixed- to floating-rate
• Primarily used to hedge interest rate risk

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Building a Fixed-Income Portfolio

• If conservative investor
• View bonds as fixed-income securities that will
  pay them a steady stream of income with little
  risk
• Buy and hold Treasury securities
• Conservative investor should consider
• Maturity, reinvestment risk, rate expectations,
  differences in coupons, indirect investing

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Building a Fixed Income Portfolio

• If aggressive investor
• View bonds as source of capital gains arising
  from changes in interest rates
• Treasury bonds can be bought on margin to further
  magnify gains (or losses)
• Seek the highest total return
• International bonds
• Direct or indirect investment
  

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Immunization

• Example

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Bond A
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Bond B
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Bond A and B if Reinvestment Rate YTM
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Bond B if Reinvestment Rate lt YTM
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Bond A if Reinvestment Rate lt YTM