货币银行与金融市场讲义-第六讲

Yields on Different Instruments:
Note: liquidity AND risk AND tax differences between these Most liquid: U.S. Treasuries Least risky: U.S. Treasuries Least taxed: Munis
Meanwhile, the return from investing $1 by strategy (b) above: = (1+ it)*(1+iet+1) - 1 = 1 + it + iet+1 + it* iet+1 - 1 = it + iet+1 + it* iet+1 ≈ it + iet+1 since it* iet+1 ≈ 0
Expectations Theory "The interest rate on a long-term bond will be the average of the shortterm interest rates that people expect to occur over the life of the long-term bond" For example, If money needed after two years, you could either a) buy a 2-year bond b) buy a 1-year bond, and then after 1 year, buy another 1-year bond If those two approaches are perfect substitutes, then the yields must equate Formally, let it = time t (today) yield on a 1-year bond i2t = time t yield on a 2-year bond iet+1 = expected yield on a 1-year bond starting in t+1 (i.e. next year) The expected return from investing $1 by strategy (a) above: = (1+ i2t)*(1+ i2t) - 1 = 1 + 2*i2t + (i2t)2 - 1 = 2*i2t + (i2t)2 ≈ 2*i2t since (i2t)2 ≈ 0
Chapter 6: The Risk and Term Structure of Interest Rates In previous chapter we analyzed the determination of "the interest rate" as if there were only 1. YTM's, though, differ according to risk and maturity, so in fact at any given time there are many interest rates. Risk Structure of Interest Rates Question: - Why do bonds with the same maturities have different YTM's? Answer: - They vary along at least three other dimensions Default Risk The perceived chance that the issuer will default (i.e. fail to live up to repayment contract) Note: U.S. Treasury bonds considered to have zero default risk (a.k.a. default-free bonds) b/c Treasury can always increase taxes or print money Definition: "risk premium" -- the additional interest people must earn in order to be willing to hold a risky bond ...the higher the default risk, the greater the risk premium Think of supply and demand analysis from last chapter (flow of funds framework for bond pricing)
Treasury Yields 1960-2006
Note how the spreads expand and contract (and occasionally go negative)
The “flight to quality” in times of crisis
Term Structure of Interest Rates Aside from differences in default risk, liquidity, and tax treatment, bonds differ along another dimension: term to maturity The "Yield Curve" Definition: A graph illustrating YTM for bonds which are comparable along all other dimensions except term to maturity.
Possible shapes of the yield curve Upward sloping (normally the case) Flat Downward sloping, or "inverted" (unusual, but important) Three Stylized Facts about the yield curve, which a good theory of interest rates must be able to explain 1. Rates tend to move together over time, even for bonds of different maturities 2. The higher the short-term rate, the more likely the yield curve is inverted 3. Yield curves almost always slope up Three Theories which attempt an explanation: 1. Expectations Theory 2. Segmented Markets Theory 3. Liquidity Premium Theory
If these two bonds are perfect substitutes then their yields must equate (else one or the other won't be held), i.e. 2*i2t = it + iet+1 or i2t = (it + iet+1)/2 In other words: the two-period (annualized) YTM must be equal to the average of the expected 1-period YTMs In the general, n-period case, the arbitrage condition would be int = (it + iet+1 + iet+2 + ... + iet+(n-1))/n Which says simply: "the interest rate on an n-period bond must be equal to the average of the expected 1-period rates over the relevant time horizon"
Note:
1. 2. 3. 4.
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rates tend to move together, though the spreads between different interest rates are not constant Munis have generally had the lowest nominal yields (higher after tax) Surge in yields on all instruments after inflationary experience of the 70s Connection between Muni “spread” and changes in income tax rates?
Note: Bonds are rated for their default risk Bond rating agencies: Moody’s, Standard & Poor’s, others
Risk Structure of Interest Rates (cont'd.) Liquidity The more widely traded, the more liquid. Treasure bonds are most widely traded, ergo most liquid Corporate bonds may face "thinner" trading markets, therefore less liquid (Note: "illiquidity" is a different kind of risk, but risk nonetheless) The more liquid, the greater the demand (ceteris paribus), and hence the higher the price (and the lower the YTM) Definition: liquidity premium -- the difference in YTM on a bond relative to a Treasury bond of equal maturity, due to the difference in liquidity. Note: Treasury bonds are the benchmark both for low default risk and for high liquidity. Thus it isn't easy to distinguish the risk premium from the liquidity premium. Usually when people say the "risk premium" they mean a combination of the two: "the risk and liquidity premium" Income Tax Considerations Recall that "Munis" are tax-free (i.e. generate no income tax liability) If you’re in the 40% tax bracket, and the yield is 10%, then your “take-home” yield is just 6%. So: risk and liquidity held constant, a person in the 40% tax bracket would be just as happy with a municipal bond paying 6% as with a non-municipal bond paying 10%