FIN 3310: Chapter 5

Which of the following statements describes a liquidity premium?

Which of the following statements describes a liquidity premium?

It is a premium that is added to the rate on a security if the security cannot be converted to cash on short notice at a price that is close to the original cost.

• A liquidity premium is a premium added to the rate on a security if the security cannot be converted to cash on short notice at a price that is close to the original cost. See 5-2: Determinants of Market Interest Rates

A bond purchased for $950 was sold for $980 after one year. The interest received during the year is $25. Which of the following is the bond's yield?

5.79%

• Yield = (Dollar income + Capital gains) ÷ Beginning value = [$25 + ($980 – $950)] ÷ $950 = 0.0579, or 5.79% See 5-1: The Cost of Money

_____ is the tendency of prices to increase over time.

Inflation

• Inflation is the tendency of prices to increase over time. The higher the expected rate of inflation, the greater the return required to compensate investors for the loss in purchasing power caused by the inflation. See 5-1: The Cost of Money

Which of the following bonds has the greatest default risk?

A CCC corporate bond with a 10-year maturity

• The CCC corporate bond with a 10-year maturity has the highest default risk as it has the poorest rating, highest interest rate risk, and the longest time to maturity. Longer maturity increases maturity risk. See 5-2: Determinants of Market Interest Rates

Following are the yields on selected Treasury securities:

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               Maturity             Yield

                 2 years                  1.6%

                 3 years                  2.2

                 4 years                  2.4

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Using the expectations theory, compute the expected one-year interest rate in Year 3. That is, compute the rate that is expected to exist only during Year 3. (Base your answer on an arithmetic average rather than a geometric average.)

3.4%

• The yield on any bond is the average of the annual, or one-year, interest rates that are expected during its life. For example, the yield on the two-year bond = (R1 + R2)/2 = 1.6%, which means that (R1 + R2) = 1.6%(2) = 3.2%, and the yield on the three-year bond = (R1 + R2 + R3)/3 = 2.2%, which means that (R1 + R2 + R3) = 2.2%(3) = 6.6%. Because the only difference between the sum of the annual rates for two years (R1 + R2) and the sum of the annual rates for three years (R1 + R2 + R3) is that the rate in Year 3 (R3) was added, the interest rate in Year 3 = 6.6% - 3.2% = 3.4% See 5-3: The Term Structure of Interest Rates

A federal deficit occurs when _____.

the government's expenses are greater than its tax revenues

• A federal deficit occurs when a government's expenses are more than its tax revenues. The government tries to control its deficit either by borrowing or by printing money. See 5-4: Other Factors That Influence Interest Rate Levels

Assume that the current interest rate on a one-year bond is 8 percent, the current rate on a two-year bond is 10 percent, and the current rate on a three-year bond is 12 percent. If the expectations theory of the term structure is correct, what is the one-year interest rate expected during Year 3? (Base your answer on an arithmetic average rather than a geometric average.)

16%

• Current interest rate on a one-year bond (R1) = 8%; Calculate R2, the one-year rate in Year 2; 10% = (8% + R2) ÷ 2; R2 = 12%; Calculate R3, the one-year rate in Year 3; 12% = (8% + 12% + R3) ÷ 3; R3 = 16%. See 5-3: The Term Structure of Interest Rates

Following is information about three bonds:

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                              Issuer                Yield             Time to Maturity

                         Treasury                 2.0%             6 months

                      Company A         5.0                     5 years

                        Company B              5.3              8 years

​

Although none of the bonds has a liquidity premium, any bond with a maturity equal to one year or greater has a maturity risk premium (MRP). Except for their terms to maturity, the characteristics of the Company A and Company B bonds are the same (including their default risk). The average inflation rate is expected to remain constant during the next 10 years. What is the annual MRP?

0.1%

The only difference between the bonds issued by Company A and Company B is the time to maturity (three years difference), which means that the difference in the yields must be due to the MRP. Thus, MRP = (Difference in yields)/(Difference in maturities) = (5.3% - 5.0%)/(8 years – 5 years) = 0.3%/3 = 0.1% See 5-2: Determinants of Market Interest Rates

You read in The Wall Street Journal that 30-day T-bills are currently yielding 8 percent. Your brother-in-law, a broker at Kyoto Securities, has given you the following estimates of current interest rate premiums:

Inflation premium          5%

Liquidity premium     1%

Maturity risk premium  2%

Default risk premium   2%

​Based on these data, the real risk-free rate of return is

Securities that can be easily converted into cash on short notice at a price that is close to the original cost generally have a _____.

low liquidity premium

• Securities that can be easily converted to cash in the market will have a low liquidity premium. Investors evaluate liquidity and include a liquidity premium (LP) when the market rate on a security is established. Higher the liquidity of an asset, lower will be the liquidity premium. See 5-2: Determinants of Market Interest Rates

Which of the following is true of the market segmentation theory?

According to the market segmentation theory, the slope of the yield curve depends on supply/demand conditions of a security in the long- and short-term markets.

• According to the market segmentation theory, the slope of the yield curve depends on supply/demand conditions of a security in the long- and short-term markets. See 5-3: The Term Structure of Interest Rates

Following is information about three bonds:

                               Issuer                Yield             Time to Maturity

                              Treasury                   2.0%            6months

                           Company A         5.0                         5 years

                           Company B              5.3                         8 years

​

Although none of the bonds has a liquidity premium, any bond with a maturity equal to one year or greater has a maturity risk premium (MRP). Except for their terms to maturity, the characteristics of the Company A and Company B bonds are the same (including their default risk). The average inflation rate is expected to remain constant during the next 10 years. What is the default risk premium (DRP) associated with the bonds issued by Company A and Company B?

2.5%

• Because they are considered default free, Treasury securities do not have default risk premiums. In the situation that is presented, the Return on the Treasury = rRF, because it has no maturity risk premium (MRP). On the other hand, the Return on the corporate bonds = rRF + MRP + DRP + LP. None of the bonds has a liquidity premium (LP), thus LP = 0. The only difference between the bonds issued by Company A and Company B is the time to maturity (three years difference), which means that the difference in their yields must be due to the MRP. Thus, MRP = (Difference in yields)/(Difference in maturities) = (5.3% - 5.0%)/(8 years – 5 years) = 0.3%/3 = 0.1% per year. Using this information, the Return on Company A’s bond = 2.0% + 5(0.1%) + DRP = 5.0%. Thus, DRP = 5.0% - 2.0% - 0.5% = 2.5%. You can check this result by computing the Return on Company B’s bond = 2.0% + 8(0.1%) + 2.5% = 5.3%, which is the number given in the table. See 5-2: Determinants of Market Interest Rates

If a stock pays a dividend of $10, and the investors need 8 percent return on their investment, then the investors should pay _____ for the stock.

$125

• Price of the stock = $10 ÷ 8% = $125. See 5-5: Interest Rate Levels and Stock Prices

Assume that a three-year Treasury note (T-note) has no maturity premium, and that the real risk-free rate of interest is 3 percent. If the T-note carries a nominal risk-free rate of return of 13 percent and if the expected average inflation rate over the next two years is 9 percent, what is the implied expected inflation rate during Year 3?

12%

• Nominal risk-free rate (r_RF ) = Real risk-free rate (r*) + Inflation premium (IP)

  13% = 3% + IP

  Average IP for next 3 years = 10%

  10% = (9% + 9% + IP₃) ÷ 3

  IP₃ = 12%

  See 5-2: Determinants of Market Interest Rates

The change in the market value of an asset over a particular time period is called the _____.

capital gain

• The change in the market value of an asset over some time period is called capital gain. Capital gain is used to calculate the return on an investment. See 5-1: The Cost of Money

Treasury securities that mature in 6 years currently have an interest rate of 8.50 percent. Inflation is expected to be 5 percent in each of the next three years and 6 percent each year thereafter. The maturity risk premium is estimated to be 0.10% × (t – 1), where t is equal to the maturity of the bond (i.e., the maturity risk premium of a one-year bond is zero). The real risk-free rate is assumed to be constant over time. What is the real risk-free rate of interest?

2.50%

• Inflation premium (IP6) = [(5% × 3) + (6% × 3)] ÷ 6 = 5.50%; Market risk premium (MRP) = 0.10% × (t – 1) = 0.10% × 5 = 0.50%; rRF = r* + MRP + IP where rRF is the nominal risk-free rate; 8.5%= r* + 0.50% + 5.50%; r* = 2.50%. See 5-2: Determinants of Market Interest Rates

You are given the following data:

r* = real risk-free rate	4%
Constant inflation premium (IP)	7%
Maturity risk premium (MRP)	1%
Default risk premium for AAA bonds (DRP)	3%
Liquidity premium for long-term Treasury bonds (T-bonds) (LP)	2%

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Assume that a highly liquid market does not exist for long-term T-bonds, and the expected rate of inflation is a constant. Given these conditions, the rate on long-term Treasury bonds is _____.

14 percent

• Nominal risk-free rate (rRF) = Real risk-free rate (r*) + Inflation premium (IP) = 4% + 7% = 11%; T-bond rate: r = r* + Inflation premium (IP) + Default risk premium (DRP) + Liquidity premium (LP) + Maturity risk premium (MRP) = 4% + 7% + 0% + 2% + 1% = 14%. Note that there is no default risk premium on a Treasury security. See 5-2: Determinants of Market Interest Rates

Your uncle would like to restrict his interest rate risk and his default risk, but he would still like to invest in corporate bonds. Which of the bonds listed below best satisfies your uncle's criteria?

An AAA bond with 5 years to maturity

• The AAA bond with 5 years to maturity has the lowest default risk because it has the best credit rating and lowest interest rate risk as it has the lowest time to maturity. See 5-2: Determinants of Market Interest Rates

Everything else equal, if the United States runs a large foreign trade deficit, the financing of the deficit will _____.

increase interest rates

• Larger trade deficits lead to an increase in interest rates. Everything else equal, trade deficits that are financed through government debt and printing of money lead to an increase in interest rates. See 5-4: Other Factors That Influence Interest Rate Levels

Assume that the expected rates of inflation over the next 5 years are 4 percent, 7 percent, 10 percent, 8 percent, and 6 percent, respectively. What is the average expected inflation rate over this 5-year period?

7%

• Average expected inflation rate = (4% + 7% + 10% + 8% + 6%) ÷ 5 = 7% See 5-2: Determinants of Market Interest Rates

Which of the following is the yield of a bond that offers a risk-free rate of 4 percent and a risk premium of 2 percent?

6%

• Bond's return (r): Yield = Risk-free rate + Risk premium = 4% + 2% = 6% See 5-2: Determinants of Market Interest Rates

Which of the following is true of the real risk-free rate of interest?

It is the rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected in the future.

• The real risk-free rate, r*, is the rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected in the future. See 5-2: Determinants of Market Interest Rates

If the Federal Reserve loosens the money supply to control growth in the economy, _____.

interest rates will decrease

• If the Federal Reserve increases the money supply through open market purchases, the amount of reserves in the banking system increases and the interest rates decrease. See 5-4: Other Factors That Influence Interest Rate Levels

Assume that real risk-free rate (r*) = 1.00%; the maturity risk premium is found as MRP = 0.20% × (t – 1), where t = years to maturity; the default risk premium for AT&T bonds is found as DRP = 0.07% × (t – 1); the liquidity premium (LP) is 0.50 percent for AT&T bonds but zero for Treasury bonds; and inflation is expected to be 7 percent, 6 percent, and 5 percent during the next three years and then 4 percent thereafter. What is the difference in interest rates between 10-year AT&T bonds and 10-year Treasury bonds? (Round answer to two decimal places.)

1.13%

• r* = 1.00%

  MRP₁₀ = 0.20% (10 – 1) = 1.80%

  DRP₁₀ = 0.07% (9) = 0.63%

  LP₁₀ = 0.50%

  Inflation premium over next 10 years (IP₁₀) = [7% + 6% + 5% + (7 × 4%)] ÷ 10 = 4.60%

  r_AT&T = r* + IP₁₀ + DRP₁₀ + LP₁₀ + MRP₁₀

  r_AT&T = 1.00% + 4.60% + 0.63% + 0.50% + 1.80% = 8.53%

  r_T-Bond = r* + IP₁₀ + MRP₁₀ + DRP₁₀ + LP₁₀= 1.00% + 4.60% + 1.80% + 0% + 0% = 7.40%

  Difference = 8.53% – 7.40% = 1.13%

  See 5-2: Determinants of Market Interest Rates

Assume that the real risk-free rate is 4 percent, and that inflation is expected to be 9 percent in Year 1, 6 percent in Year 2, and 4 percent thereafter. Also, assume that all Treasury bonds are highly liquid and free of default risk. If 2-year and 5-year Treasury bonds both yield 12 percent, what is the difference in the maturity risk premiums (MRPs) on the two bonds, i.e., what is MRP₅ – MRP₂? (Round answer to one decimal place.)

2.1%

• Treasury yield (r_t) = 4% + Inflation premium (IP_t) + Market risk premium (MRP_t)

  Inflation premium for the 5-year bond = (9% + 6% + 4% + 4% + 4%) ÷ 5 = 5.4%

  Inflation premium for the 2-year bond = (9% + 6%) ÷ 2 = 7.5%

  r₅ = 4% + 5.4% + MRP = 12%

  MRP₅ = 12% – 9.4% = 2.6%

  r₂ = 4% + 7.5% + MRP =12%

  MRP₂ = 12% – 11.5% = 0.5%

  Difference = (2.6% – 0.5%) = 2.1%

  See 5-2: Determinants of Market Interest Rates