ECN 325 Exam 2

2) Consider a one-year corporate bond that has a 20% probability of default. The payoff onthe bond is $2,000 if the corporation does not default. The interest rate is 10%. If buyers of thisbond are risk-neutral, this bond will sell forA) $400.B) $909.09.C) $1,454.54.D) $1,600.

$1,454.54.

Fly-By-Night Inc. issues $100 face value, zero-coupon, one-year bonds. The currentreturn on one-year, zero-coupon U.S. government bonds is 3.5%. If the Fly-By-Night bonds areselling for $92.00, what is the risk premium for these bonds?A) 8.7%B) 1.5%C) 5.2%D) 8.0%

5.2%

.8) A $500 investment has the following payoff frequency: half of the time it will pay $350and the other half of the time it will pay $900. Its standard deviation and value at risk,respectively, areA) $275; $150.B) $625; $275.C) $275; $350.D) $125; $500.

A) $275; $150.

Consider a one-year, 10-percent coupon bond with a face value of $1,000 issued by a privatecorporation. The one-year risk-free rate is 10 percent. The corporation has hit on hard times,and the consensus is that there is a 20 percent probability that it will default on its bonds. Ifan investor were willing to pay at most $775 for the bond, is that investor risk-neutral orrisk averse?

Answer: If the bond were risk free, it would pay off $1,100 in one year's time - $100 couponpayment and $1,000 face value of the bond.If there is a 20% risk of default, then the expected value of these payment flows associatedwith the bond are ($1,100 × 0.8) + ($0 × 0.2) = $880The present value of $880 in one year's time is $880/1.1 = $800. This would be the price arisk-neutral investor would be willing to pay.If the investor is willing to pay at most $775 for the bond, he or she requires compensationfor bearing the risk associated with the bond and so is risk averse.

Assume that the economy can experience high growth, normal growth, or recession. Underthese conditions, you expect the following stock market returns for the coming year: (LO2,LO3)State of the Economy Probability ReturnHigh Growth 0.2 +30%Normal Growth 0.7 +12%Recession 0.1 -15%a. Compute the expected value of a $1,000 investment over the coming year. If you invest$1,000 today, how much money do you expect to have next year? What is the percentageexpected rate of return?b. Compute the standard deviation of the percentage return over the coming year.c. If the risk-free return is 7 percent, what is the risk premium for a stock marketinvestment?

Answer:a. Expected Value = 0.2($1,000)(1 + 0.30) + 0.7($1,000)(1 + 0.12) + 0.1($1,000)(1- 0.15) = $1,129 Expected Percentage Return = 0.2(0.30) + 0.7(0.12) + 0.1(-0.15) = 0.129, or 12.9%Alternatively, [(1,129 -1,000)/1,000] × 100 = 0.129, or 12.9%b. Standard Deviation= 11.7% c. Risk Premium = 12.9% - 7% = 5.9%%7.11%)9.1215(1.0

Explain why two countries with the same average rate of inflation may not present thesame inflation risk for holders of those countries' bonds?

As the text points out, while the expected (or average) inflation canbe the same, the standard deviation around this expected rate presentsdifferent amounts of risk. The higher the standard deviation, the greaterthe risk. For countries where inflation is volatile, the standard deviationaround their average expected rate will be greater, and therefore theirbonds will present greater inflation risk

Luis is a risk-averse investor who is considering Proposal A and Proposal B. Eachproposal requires the same amount of investment and has equivalent expected values. However,the distribution of possible payoffs for Proposal A is more spread out than the distribution ofpossible payoffs for Proposal B. Based on this information, Luis should chooseA) Proposal A.B) Proposal B.C) either since they are equivalent.D) neither there is too much risk involved.

B Proposal B

5) The greater the standard deviation of an investment, theA) lower the return.B) greater the risk.C) lower the risk.D) lower the risk and return.

B greater the risk.

7) A $600 investment has the following payoff frequency: a quarter of the time it will be $0;three quarters of the time it will pay off $1,000. Its standard deviation and value at risk,respectively, areA) $750; $600.B) $433; $600.C) $0; $1,000.D) $433; $1,000

B) $433; $600

1) An investor puts $1,000 into an investment that will return $1,250 one-half of the timeand $900 the remainder of the time. The expected return for this investor isA) $1,075.B) 5.0%.C) 7.5%.D) 15.0%.

C 5.0%

The difference between standard deviation and value at risk is A) nothing, they are two names for the same thing.B) value at risk is a more common measure in financial circles than is standarddeviation.C) standard deviation reflects the spread of possible outcomes, whereas value at riskfocuses on the value of the worst outcome.D) value at risk is expected value times the standard deviation.

C) standard deviation reflects the spread of possible outcomes, whereas value at riskfocuses on the value of the worst outcome

The following figure illustrates two different options for investing $1,000 where theexpected value is equal for both. Which one is riskier?A) Case 1B) Case 2C) The risk is equal between the two cases.D) More information is needed to compare the risk.

Case B

An investment pays $1,000 three quarters of the time, and $0 the remaining time. Itsexpected value and variance respectively areA) $1,000: 62,500 dollars 2B) $750; 46,875 dollarsC) $750; 62,500 dollarsD) $750; 187,500 dollars 23)

D 750; 187,500 dollar^2

13) If you were going to issue bonds, would you prefer to be in a country where the averageinflation rate is 3% inflation but fluctuates wildly, or in a country with a higher, 4% expected inflation rate is that stable

Even though the 4% expected rate is higher, it is stable. As we saw,the inflation risk isn't really the risk from inflation; it is the risk thatresults from unexpected changes in inflation which then cansignificantly alter the real interest rate, and therefore the real returnsbondholders receive. Because bondholders tend to be risk-averse, theywould want to be compensated for the inflation risk, and since theinflation risk results from the fluctuations in the rate of inflation, thereturns required by bondholders in the country where the averageexpected rate is 3% but volatile are likely to be higher than the requiredreturns on the bonds in the higher but stable inflation country. Thisexplains, at least partially, why the central banks in many developedcountries strive for inflation stability. Stable prices will lead to lowerinflation risk and a more efficient bond market

5) Which of the following is true of interest-rate risk?A) It is the risk that the coupon rate for a bond will change, affecting currentbondholders' coupon payments.B) It refers to the probability that a borrower will default on debt obligations.C) It is the risk that the face value of a bond will change before maturity.D) Individuals owning long-term bonds are exposed to greater interest-rate risk

Individuals owning long-term bonds are exposed to greater interest-rate risk

Carolina is considering a $500 investment that will pay $750 with a 30% probability,$600 with a 20% probability, and $350 with a 50% probability. Construct a table showing herprobabilities and payoffs and solve for the expected value of her investment option.

Possibilities Probability Payoff Probability × Payoff1 0.3 $750 $2252 0.2 $600 $1203 0.5 $350 $175E xpected value = $225 + $120 + 175 = $520

Explain why the bid-ask spread (which is the difference in price a dealer is willing to buythe bond for and the price at which the dealer sells the bond) on most municipal bonds would begreater than the spread on U.S. Treasury bonds

Spreads are the difference between the dealer's bid and asked prices.Since dealers are ready to buy or sell the bond, they must carry aninventory, which means they accept risk just like any other bondholderwould. One of these risks is liquidity risk, which is the risk of not beingable to sell the bond when you would like. Since the market for U.S.Treasury bonds is far more liquid than would be the market for anysingle municipal bond, the dealer of the municipal bond would facegreater liquidity risk and require a larger spread

At the time the government of Bulgrovia issued new bonds, they issued them at a pricethat reflected the risk-free rate because investors had no concerns regarding default risk, so didnot require a risk premium. That risk-free rate was 4%. These bonds currently have one year tomaturity and you notice the yield is 20%. Can you calculate the probability that the Bulgroviangovernment will default?13) If you were going to issue bonds, would you prefer to be in a country where the averageinflation rate is 3% inflation but fluctuates wildly, or in a country with a higher, 4% expected

The simple answer is no. A risk-premium is a measure of thepremium required by investors to accept risk; it is not a direct measureof the risk of default. We could only determine this if investors are risk-averse. If that were true then, we can calculate the probability fairlyeasily by realizing the probability the bond will not default can beexpressed by 1.04/1.20, which equals 0.867. If we subtract this from 1.0we obtain the probability of default, which is 0.133

3) A student receives a five-year loan to pay for a $2,000 used car. The lender and thestudent agree to an 8% interest rate on a fixed-rate loan. Expected inflation was estimated toequal 2.5%, but it unexpectedly decreases to 2%. Which one of the following is true?A) The real interest rate decreased.B) The student is made worse off because her real cost of borrowing is higher.C) The lender is made worst off because his real return on the car loan is lower.D) Both the student and the lender benefit.

The student is made worse off because her real cost of borrowing is higher.

The text identified the various sources of risk for bonds. Are U.S. Treasury TIPS bondsfree from risk? Explain.

These bonds are free from two of the main sources of risk that makeholding bonds risky. U.S. Treasury bonds are free from default risk, andthe TIPS bonds also remove the inflation risk. However, the risk stillpresent with these bonds is the interest-rate risk. If the bondholder doesnot plan on holding these bonds until maturity, changes in the interestrate (specifically increases) can result in capital losses or returns less than expected

10) Interest-rate risk would not matter to a holder of aA) U.S. government bond.B) U.S. government bond indexed for inflation.C) U.S. government bond who plans on selling it in one year.D) U.S. government bond that plans on holding it until it matures.

U.S. government bond that plans on holding it until it matures.

Consider the following bonds. Which is subject to the greatest interest-rate risk?A) a 30-year fixed-rate mortgage (fixed payment loan)B) a consolC) a Treasury billD) a 20-year corporate bond

a consol

.9) Interest-rate risk results fromA) bond prices being fixed over the life of the bond.B) a mismatch between an individual's investment horizon and a bond's maturity.C) the fact that most people hold bonds until they mature.D) inflation being uncertain

a mismatch between an individual's investment horizon

A 10-year zero-coupon bond has a yield of 6 percent. Through a series of unfortunatecircumstances, expected inflation rises from 2 percent to 3 percent. The face value of thebond is $100.

a. Assuming the nominal yield rises in an amount equal to the rise in expected inflation,compute the change in the price of the bond.b. Suppose that expected inflation is still 2 percent, but the probability that it will move to 3percent has risen. Describe the consequences for the price of the bond.Answer:a. Price (with 2% expected inflation) = 100/(1.06)10 = $55.84Price (with 3% expected inflation) = 100/(1.07)10 = $50.83The price has fallen by $5.01b. There is increased inflation risk. Investors will require compensation for taking onadditional risk, so the price will fall and the yield will rise.

Inflation risk results from risk that the bond's return differs from the risk-free rate.B) a mismatch between an individual's investment horizon and a bond's maturity.C) the difficulty an investor may face in selling a bond before it matures.D) an investor's uncertainty about the real value of the payments that occur over time

an investor's uncertainty about the real value of the payments that occur over time

2) Consider two investors: one is risk-neutral and the other is risk-averse. How do they eachassess a risk premium?

he risk-neutral investor seeks a risk premium that has the price ofthe bond (and its subsequent yield) such that the price equals theexpected value (the sum of the payoffs times the probabilities). The risk-averse investor would offer a price less than this (and therefore seek ahigher yield) since he/she requires additional compensation for risk.Therefore, the risk-averse investor's risk premium would be greater

6) The U.S. Treasury issues bonds where the return is indexed to the consumer price index.We should expect that these bonds, relative to other U.S. Treasury bonds, will haveA) lower price and lower return due to the decreased risk.B) lower price and a lower fixed return since the demand for them should be higher.C) higher price and higher fixed return since we always seem to have some inflation.D) higher price and lower return due to the decreased risk from inflation in holding these bonds

higher price and lower return due to the decreased risk from inflation in holding these bonds

U.S. government bonds that provide for bondholders to receive a fixed rate of interestplus the change in the consumer price index were designed to removeA) default risk.B) liquidity risk.C) inflation risk.D) interest-rate risk..

inflation risk