CHAPTER 6: Interest Rates - Po-Hsuan (Paul) Hsu What’re interest rates? Determinants of interest rates The term structure and yield curves

What’re interest rates (r)? Interest is a charge for borrowed capital. Interest rates vary across different types of money borrowed (debt securities) – why? 3 major money borrowers: 1. Banks (checking, saving, CD) 2. Governments (Fed, State, City) 3. Firms/corporates

The duration of the money borrowed: 1. Short-term (1m, 3m, 6m, 9m) 2. Long-term (1y, 2y, 3y, 5y, 10y, 30y, etc.) We mainly discuss the following 4 types of debt securities: 1. Government: Long-term (T-bonds), short-term (T-bills). “T” denotes treasury 2. Corporate: Long-term bond, short-term (notes)

“Nominal” vs. “real” interest rates r = represents any nominal rate r* = represents the “real” risk-free rate of interest. ? What’s the most secured debt?

Determinants of interest rates r = r* + IP + DRP + LP + MRP r = required/expected return on a debt security r* = real risk-free rate of interest – existing? IP = inflation premium DRP = default risk premium LP = liquidity premium – Corporate only MRP = maturity risk premium – Corporate only

Premiums added to r* for different types of debt IP MRP DRP LP Short-term Treasury  Long-term Treasury Short-term Corporate Long-term Corporate

Treasury bills and bonds: Hypothetical T-bond yield curve Years to Maturity Real risk-free rate 5 10 15 1 10 20 Interest Rate (%) Maturity risk premium Inflation premium An upward sloping yield curve. Upward slope due to an increase in expected inflation and increasing maturity risk premium.

Calculating inflation premium (IP) IP for future t years: Find the average expected inflation rate (INFL) over years 1 to t:

Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter. IP1 = 5% / 1 = 5.00% IP10= [5% + 6% + 8%(8)] / 10 = 7.50% IP20= [5% + 6% + 8%(18)] / 20 = 7.75% - Any nominal r must earn these IPs to break even vs. inflation

Computing maturity risk premium (MRP) Find the appropriate maturity risk premium (MRP). The following equation will be used to find a bond’s MRP at t:

Using the given equation: MRP1 = 0.1% x (1-1) = 0.0% MRP10 = 0.1% x (10-1) = 0.9% MRP20 = 0.1% x (20-1) = 1.9% Notice that the MRP is increasing in t (as the time to maturity increases), as it should be.

Add the IPs and MRPs to r* to construct the T-bond yield curve By adding IP and MRP to r*: rt = r* + IPt + MRPt Assume r* = 3%, r1 = 3% + 5.0% + 0.0% = 8.0% r10 = 3% + 7.5% + 0.9% = 11.4% r20 = 3% + 7.75% + 1.9% = 12.65%

Pure Expectations Hypothesis (PEH) The yield curve reflects the market’s expectation of “future interest rates” We can break down a long-term interest rate into an average of current short-term rates and future short-term rates

An example: Observed Treasury rates and the PEH Maturity Yield 1 year 6.0% 2 years 6.2% 3 years 6.4% 4 years 6.5% 5 years 6.5% If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now? Three-year securities, two years from now?

One-year forward rate (i.e. future one-year interest rate) 6.0% x% 0 1 2 6.2% (1.062)2 = (1.060) (1+x) 1.12784/1.060 = (1+x) 6.4004% = x PEH says that one-year securities will yield 6.4004%, one year from now.

Three-year security, two years from now 6.2% x% 0 1 2 3 4 5 6.5% (1.065)5 = (1.062)2 (1+x)3 1.37009/1.12784 = (1+x)3 6.7005% = x PEH says that three-year securities will yield 6.7005%, two years from now. Note: You may want to learn how to use Yx in your financial calculator!!

How about corporate bond yields? Corporate and Treasury yield curves Interest Rate (%) 15 BB-Rated 10 AAA-Rated Treasury Yield Curve 6.0% 5 5.9% 5.2% Years to Maturity 1 5 10 15 20

Compare T-bill to short-term corporate bond Interest rate (yield) LP DRP 1-year T-bill 4.65% - 1-year AAA ? % 0.10% 0.40% 1-year BBB 0.20% 0.80% Hint: Page 5 of this handout!

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Other factors that influence interest rate levels Federal reserve policy Federal budget surplus or deficit Level of business activity International factors

Risks associated with investing overseas Exchange rate risk – If an investment is denominated in a currency other than U.S. dollars, the investment’s value will depend on what happens to exchange rates. Country risk – Arises from investing or doing business in a particular country and depends on the country’s economic, political, and social environment.

Top 5 countries (least risk) Country risk rankings Top 5 countries (least risk) Rank Country Score 1 Switzerland 95.2 2 Luxembourg 93.9 3 United States 93.7 4 Norway 5 United Kingdom 93.6 Bottom 5 countries (most risk) Rank Country Score 169 Afghanistan 11.0 170 Liberia 9.4 171 Sierra Leone 9.3 172 North Korea 8.9 173 Somalia 8.2 Source: “Country Ratings by Region,” Institutional Investor, www.institutionalinvestor.com, September 2004.