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MTSU Econ 3210 - Chapter 5

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Stuart Fowler

on 18 September 2014

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Transcript of MTSU Econ 3210 - Chapter 5

Chapter 5, The Risk Structure and Term Structure of Interest Rates.
Why Do Bonds With the Same Maturity Have Different Interest Rates? The Information in Bond Prices
Recall that the bond market was fictitious. But we can break of the market in to different segements.
Why Do Similar Bonds But With Different Maturities Have Different Interest Rates?
Demand
The Market for Bonds;
equilibrium price and quantity
Price
Quantity
Supply
Pe
Qe
Risky Bonds
Higher Taxed Bonds
Less Liquid & High Information Costs Bonds
We know from chapter 4 that risk reduces the demand for bonds. Within bonds, riskier bonds should have lower prices and thus higher returns.
Risky Bond
Safe Bond
Economists at bond rating agencies rate bonds based on the issuer's (seller) likely ability to make the required payments on its bonds.

There are three main bond rating companies: Moody's, Standard & Poor's, and Titch Ratings.

Each has a grading system:
In general, US Treasuries are rated safe (AAA)
Non-Investment grade are called junk. Prices should be different:
Note: The above graph shows what would happen in a recession. If the risk premium is the difference between Baa and Treasury bond yields, then the risk premium should rise in riskier times:
Moody's may downgrade US debt:
Taxes reduce the expected return of bonds. We know from chapter 4 that reduction in expected return reduces the demand for bonds. Within bonds, higher taxed bonds have lower prices and thus higher returns.
Municipal bonds are not subject to any taxes. Treasury bonds are only subject to federal taxes.
Corporate bonds are subject to federal, state, and local.
Q: Suppose federal taxes on bonds increase. Show what happens to muni and treasury yields.
Q: would municipalities like or dislike increases in federal taxes? Explain your reasoning.
An increase in a bond’s liquidity or a decrease in the cost of acquiring information about the bond will increase the demand for the bond.
Ex: During the financial crisis of 2007-2009, homeowners were defaulting on many of the mortgages contained in the bonds. To make matters worse, investors came to realize that they did not fully understand these bonds and had difficulty finding information contained in the mortgage-backed bonds.
Q: Treasuries are, in general, considered riskless. Why then would some treasuries pay higher interest rates (yields)?
Consider the following U.S. Treasuries from bloomberg. You should see:
A 1yr T-bill has an annual yield of 0.14% or 0.0014.
A 3yr T-bond has an annual yield of 0.625% or 0.00625.
Before we get to the implications of the different yields, we first ask how bloomberg.com computes bond yields.
Bloomberg ask dealers for prices on T-bills and T-bonds.
Once it has the prices, it computes the yields using the PV formulas derived in Chapter 3.

Ex: Bloomberg finds the price of 1yr t-bill of P=99.8602. Assuming a par of 100, the yield is found by:
100/(1+i)=99.8601, or i = 0.0014

Ex: bloomberg finds the price of a 3yr bond with par 100 and coupon rate of 0.00625 equal to P = 100.0148. The yield is found by:
100.0148= 0.625/(1+i)+0.625/(1+i)^2+100.625/(1+i)^3
i=0.0062
The puzzle
The graph in the treasuries sheet plots the yield curve

Def: The Treasury yield curve shows the relationship on a particular day among the interest rates on Treasury bonds with different maturities.

Def: When short-term rates are lower than long-term rates, we have an upward-sloping yield curve.

Def: when short-term interest rates are higher than long-term interest rates, resulting in a downward-sloping yield curve.
Because longer term bonds may be less liquid, long term bond should have lower prices and hence higher yields. Also, long term bonds involve more opportunity costs. Thus, should have lower prices.

Def: The term premium is the extra return on longer maturity bonds from liquidity differences and opportunity costs of money.

Q: If longer maturity bonds should have lower prices, why does the yield curve invert from time to time?
downward=inverted
Besides the term premium, there is another reason for the slope of the yield curve; EXPECTATIONS ABOUT FUTURE RATES.

Q: An investor wants to save for two years. What are her options for saving by bonds?
A: She could buy a 2yr bond. Or, buy a 1yr today, then another 1yr bond next year.

Q: Suppose the opportunity cost of money was zero and there are no liquidity differences (term premium=0). How would you save?
A: Choose the one with the highest average return!

Expectations and the Yield Curve
An Example: mortgage bond CWABS 2006-7
Typical Borrowers from Florida & California
Example 1: Save by buying two year bond is plan A. Save by buying 1 year bond twice is plan B. What is the average annual return of either plan.
Let:

i1 = current annual rate on 1 year bond
i2 = current annual rate on 2 year bond
i1^ex = annual rate expected on 1 year bond in 1 year
Plan A
Plan B
i2 = .10
i1 = .05
i1^ex = .10
Avg annual return=
Plan A
Plan B
i2 = .10
i1 = .05
i1^ex = .15
Avg annual return=
Example 2: What is the average annual return of either plan.
Example 3: What is the average annual return of either plan.
Plan A
Plan B
i2 = .10
i1 = .05
i1^ex = .25
Avg annual return=
Rule: If we see savers buying both bonds, then the three returns should be related by:

i2 = [i1 + i1^ex]/2
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