CHAPTER 6: Interest Rates

- Po-Hsuan (Paul) Hsu    What’re interest rates?

Determinants of interest rates The term structure and yield curves

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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.

3.

Governments (Fed, State, City) Firms/corporates

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 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)

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“ Nominal” vs. “real” interest rates r = represents any nominal rate r* = represents the “real” risk-free rate of interest.

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What’s the most secured debt?

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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

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

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Treasury bills and bonds: Hypothetical T-bond yield curve

Interest Rate (%) 15 10 5 0 Maturity risk premium Inflation premium

  An upward sloping yield curve.

Upward slope due to an increase in expected inflation and increasing maturity risk premium.

Real risk-free rate Years to 1 10 20 Maturity 6-7

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

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Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter.

IP 1 = 5% / 1 = 5.00% IP 10 = [5% + 6% + 8%(8)] / 10 = 7.50% IP 20 = [5% + 6% + 8%(18)] / 20 = 7.75% - Any nominal r must earn these IPs to break even vs. inflation

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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: MRP t  0.1% ( t 1 )

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Using the given equation: MRP 1 MRP 10 = 0.1% x (1-1) = 0.0% = 0.1% x (10-1) = 0.9% MRP 20 = 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.

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Add the IPs and MRPs to r* to construct the T-bond yield curve By adding IP and MRP to r*: r t = r* + IP t + MRP Assume r* = 3%, t r 1 r 10 r 20 = 3% + 5.0% + 0.0% = 8.0% = 3% + 7.5% + 0.9% = 11.4% = 3% + 7.75% + 1.9% = 12.65%

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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

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An example: Observed Treasury rates and the PEH Maturity 1 year 2 years 3 years 4 years 5 years Yield 6.0% 6.2% 6.4% 6.5% 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?

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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.

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Three-year security, two years from now 6.2% x% 0 1 2 3 4 5 6.5% (1.065) 5 1.37009/1.12784

6.7005%   = (1.062) 2 = (1+x) 3 = x (1+x) 3 PEH says that three-year securities will yield 6.7005%, two years from now.

Note: You may want to learn how to use Y x calculator!!

in your financial

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How about corporate bond yields? Corporate and Treasury yield curves

Interest Rate (%) 15 10 5 5.2% 5.9% BB-Rated AAA-Rated 6.0% Treasury Yield Curve 0 0 1 5 10 15 20 Years to Maturity 6-17

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

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End

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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

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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.

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Country risk rankings

Top 5 countries (least risk) Rank Country Score 1 2 Switzerland Luxembourg 95.2

93.9

3 4 5 United States Norway United Kingdom 93.7

93.7

93.6

Bottom 5 countries (most risk) Rank Country 169 Afghanistan 170 Liberia 171 Sierra Leone 172 North Korea 173 Somalia Source: “Country Ratings by Region,” Institutional Investor, www.institutionalinvestor.com, September 2004.

Score 11.0

9.4

9.3

8.9

8.2

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