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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. Governments (Fed, State, City) 3. 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.

? 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 premiumDRP = default risk premiumLP = liquidity premium – Corporate onlyMRP= maturity risk premium – Corporate

only

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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

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Treasury bills and bonds:Hypothetical T-bond yield curve

An upward sloping yield curve.

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

Years to Maturity

Real risk-free rate

0

5

10

15

1 10 20

InterestRate (%)

Maturity risk premium

Inflation premium

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Calculating inflation premium (IP) IP for future t years: Find the average

expected inflation rate (INFL) over years 1 to t:

t

INFLIP

t

1ii

t

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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

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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:

) 1 -t ( 0.1% MRPt

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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.

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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*:

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%

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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 Yield1 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?

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One-year forward rate (i.e. future one-year interest rate)

(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.

0 1 2

6.0% x%

6.2%

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Three-year security, two years from now

(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!!

0 1 2 3 4 5

6.2% x%

6.5%

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How about corporate bond yields? Corporate and Treasury yield curves

0

5

10

15

0 1 5 10 15 20

Years toMaturity

Interest Rate (%)

5.2%5.9%

6.0%TreasuryYield Curve

BB-Rated

AAA-Rated

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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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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 Switzerland 95.2

2 Luxembourg 93.9

3 United States 93.7

4 Norway 93.7

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 8.2Source: “Country Ratings by Region,” Institutional Investor, www.institutionalinvestor.com, September 2004.