Relationship among rates on bonds with different characteristics but same maturity. What causes interest rates on bonds with the same maturities to increase? Risk (default or credit) ↑: likelihood that issuer will not be able to service debt Measured by default risk premium above Treasury with the same maturity. Credit rating agencies provide information on the creditworthiness of issuer. Liquidity ↓: Desired by investors who accept lower rate on more liquid investments. Information costs ↑: Reduces the bond’s expected return. Taxation ↑: Investors interested in after tax return (interest taxed as income, capital gains at lower rate). Municipal bonds issued by states and municipalities. Demand for Munis & T-bonds ↑ & ↓ with federal income tax. The Risk Structure of Interest Rates

Bond Rating a single statistic summarizing a agency’s (modern started with Moody’s Analyses of Railroad Investments in 1909) view of the issuer’s ability to service bonds. By the late 1970s, recession, inflation, and government regulations expanded the work of credit rating agencies. When credit rating agencies began charging issuers—rather than investors—for their services, a conflict of interest emerged. Credit rating agencies came under increased scrutiny in the financial crisis. Alternatively, ratings were accurate when issued but creditworthiness declined rapidly after housing bust and the financial crisis. In 2010, Congress passed the Dodd-Frank Act that affected the regulations of credit rating agencies, and created a new office within the SEC to oversee credit rating agencies.

Changes in Default Risk and in the Default Risk Premium The initial default risk premium is the yield difference due P 1 T - P 1 C difference. Higher corporates’ default risk shifts demand for corporates/Treasuries to left/right.

Changes in Default Risk and in the Default Risk Premium The corporate is for Baa-rated bonds. The Treasury is for 10-year Treasury notes. The default premium typically rises in recession, which can cause a flight to quality. The default premium increased more in the than the 2001 recession.

Relationship among the rates on similar bonds with different maturities. Treasury yield curve: ytm on zero coupon T-bonds with different maturities. Upward/downward-sloping yield curve: short-term than long-term rates. The Term Structure of Interest Rates Most of the time since 1970, 3-month T- bills rates were below the rates on 10-year T-notes, but they tend to move together Treasury yield curves

Explaining the Term Structure Has to be able to account for three facts: 1. Rates on long-term bonds are usually higher than on short-term bonds. 2. Rates on short-term bonds are occasionally higher than on long-term bonds. 3. Interest rates on bonds of all maturities tend to rise and fall together. Economists have advanced three theories to explain these facts: Expectations theory: bond’s long-term rate is average of E(rates) on short-term bonds. Investors in the bond market have the same investment objectives. Different maturity bonds are perfect substitutes. Segmented markets theory: bond rate = f(demand & supply of bonds of that maturity). Investors in the bond market do not all have the same objectives. Different maturity bonds are not perfect substitutes and investors market for bonds of one maturity do not participate in markets for other maturity bonds. More invest in short-term bonds (less risk) cause their prices ↑ and their % ↓ than long-term bonds making typical yield curve upward-sloping. But cannot explain downward-sloping curve or why all maturities % tend to move together. Liquidity premium (or preferred habitat) theory: Expectations theory + Term premium (additional rate require to buy a long-term bond than a sequence of short-term bonds).

The Expectations Theory Applied in a Simple Example with Zero Coupon Bond Two strategies for investing $1,000 for 2 years have the same return (arbitrage): 1. The buy-and-hold strategy: $1,000(1 + i 2t )(1 + i 2t ). 2. The rollover strategy: $1,000(1 + i 1t )(1 + i e 1t+1 ). (1+i 2t ) 2 = (1+i 1t )(1+i e 1t+1 ) => 1+2*i 2t +i 2t 2 = 1+i 1t +i e 1t+1 +i 1t *i e 1t+1 => i 2t ≈ (i 1t +i e 1t+1 ) / 2 i nt ≈ (∑i e 1t+n ) / n With compounding the exact formula is:i 2t = [(1+i 1t )(1+i e 1t+1 )] 1/2 - 1 i nt = [∏(1+i e 1t+n )] 1/n - 1 Alsoi e 1t+1 = (1+i 2t ) 2 / (1+i 1t ) - 1 ≈ 2*i 2t - i 1t i e 1t+n = (1+i nt ) n / (1+i nt-1 ) n ≈ n*i nt - ∑i nt-1 Liquidity Premium Theory Adds Term Premium i 2t ≈ (i 1t +i e 1t+1 ) / 2 + i tp 2t or i nt ≈ (∑i e 1t+n ) / n + i tp nt i e 1t+1 ≈ 2(i 2t - i tp 2t ) - i 1t ori e 1t+n = (1+i nt ) n /(1+i nt-1 ) n ≈ n(i nt - i tp nt ) - ∑i nt-1

Using the Expectations and Liquidity Premium Theory to Find Expected Rates What are the expected 1-year T-bill rates in 2 and 3 yrs if 1, 2 and 3 year T-note rates are 1.25%, 2% and 2.5%, while the 2 and 3 yr term premiums are 0.20% and 0.40%? Expectations Theory i 2t = 2% ≈ (i 1t + i e 1t+1 ) / 2 = (1.25% + i e 1t+1 ) / 2 => i e 1t+1 ≈ 2*i 2t - i 1t = 2*2% % = 2.75% i 3t = 2.5% ≈ (i 1t + i e 1t+1 + i e 1t+2 ) / 3 = (1.25% % + i e 1t+2 ) / 3 => i e 1t+2 ≈ 3*i 3t - i 1t - i e 1t+1 = 3*2.5% % % = 3.5% Liquidity Premium Theory i 2t = 2% ≈ (i 1t + i e 1t+1 ) / 2 + i tp 2t = (1.25% + i e 1t+1 ) / % => i e 1t+1 ≈ 2(i 2t - i tp 2t ) - i 1t = 2(2% - 0.2%) % = 2.35% i 3t = 2.5% ≈ (i 1t + i e 1t+1 + i e 1t+2 ) / 3 + i tp 3t = (1.25% % + i e 1t+2 ) / % => i e 1t+2 ≈ 3(i 3t - i tp 3t ) - i 1t - i e 1t+1 = 3(2.5% - 0.4%) % % = 2.7%

Interpreting the Term Structure Using the Expectations Theory The expectations theory implies: Upward-sloping yield curve: investors expecting future short-term rates to be above the current short-term rate. Problem: short-term % as likely to fall or rise at any time. Flat yield curve: investors expecting future short-term rates to equal the current short-term rate. Downward-sloping yield curve: investors expecting future short-term rates to be lower the current short-term rate.

Can You Make Easy Money from the Term Structure? The term interest carry trade refer to borrowing at a low short-term interest rate and using the borrowed funds to invest at a higher long-term interest rate. a.Would you use an interest-carry-trade strategy for your personal investments? Identify the difficulties with this strategy for an individual investor. Seems a good investment with typical upward sloping yield curve. But gap between short-term and long-term rate is too small for individuals. b.If you were an investment adviser for an institutional investor, would you advise that investor to use an interest-carry-trade strategy? Identify the difficulties with this strategy for an institutional investor. Institutional investors borrow at lower short-term % & have less default risk. But this would not bring potential profits because of expectations theory (average of E(short-term rates) roughly equals equivalent long-term rates). b.If the yield curve was inverted, or downward sloping, would an institutional investor still find an interest-carry-trade strategy to be possible? Briefly explain. Institutional investor could borrow long-term and invest at short-term rates. But investor would face reinvestment risk—that the rate on new short-term investments will declined after the short-term investment mature.

Theories of Term Structure – Summary

Can the Term Structure Predict Recessions? During every recession since 1953, the term spread between the yields on long-term and short-term Treasury securities narrowed significantly, because during recessions, rates typically fall, but more so for short-term than long- term bonds. In this situation, the liquidity premium theory predicts that long-term rates should fall relative to short-term rates, making the yield curve inverted.