5-2

The short term interest rate are more volatile then the long term interest rate so short term prices are more sensitive to interest changes than are long term bonds prices. True or false? Explain.

Answer: The statement is false. The possibility of interest rates change is higher in long run than in the short run. Therefore bonds with longer maturity period might need to sell in discount price or interest rate might go down/up. While in short run risk of changes (increase/decrease) in interest rate is low because possibility of significantly change in interest rate is very low. Since short term bond mature within 12 months it is convenient for investor to hold till maturity where as long term bond has maturity period 10 to 15 years and might need to sell in between and investor might have to sell their bonds on discount price. Hence long term bond prices are more sensitive to interest rate changes than are short term bonds price.

5-3

The rate of return you would get if you bought a bond and held it to its maturity date is called the bond’s yield to maturity. If interest rates in the economy rise after a bond have been issued, what will happen to the bond’s price and to its YTM? Does the length of time to maturity affects the extent to which a given change in interest rates will affect the bond’s price?

Answer: If interest rates in the economy rise after a bond have been issued then bonds price will fell down because bond will pay less coupon interest than newly issued bonds hence bond would be offer in price below par.

If interest rate in the economy rises yield to maturity also rises because yield to maturity and market interest rate is the same. Yield to maturity is sum of current yield and positive/negative capital gains yield. When market interest rate fall the price of bonds goes down that makes positive capital gain and hence increases yield to maturity.

Yes, length of time to maturity affects extent to which a change in interest affects the bond’s price. Bonds with longer term to maturity tend to have higher increase/decrease in to bond’s prices given the changes in interest rate than bonds with shorter term to maturity.

5-4

If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain.

Answer: If interest rate decline in the market, the value of callable bonds will not rise as much as regular bond (bonds with no call option). The reason is that issuer of bonds has option to redeems the bond any time and when interest rate decline in the market this is the perfect time for them to redeem the bonds with high interest rate and issue new bonds with low prevailing market interest rate.

6-3

Suppose you owned a portfolio consisting of $250,000 worth of long-term U.S. Government bonds.

a. Would your portfolio be riskless?

Answer: While discussing about risk of portfolio it is necessary to know different types of risk that a portfolio could have. Some of the risk that security (portfolio) has is default risk, liquidity risk, inflation risk and others. U.S government bonds are backed by U.S government therefore these bonds does not have default risk and liquidity risk but in the long term inflation might increased significantly and interest rate might go up that cause the inflation premium (difference between expected and actual inflation rate) to go up. Due to high inflation the value of portfolio may worth less in long-run. Hence a portfolio consisting of long-term U.S government bonds are not riskless.

b. Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury bills. Every 30 days your bills mature, and you reinvest the principal ($250,000) in a new batch of bills. Assume that you live on the investment income from your portfolio and that you want to maintain a constant standard of living. Is your portfolio truly riskless?

Answer: 30-day Treasury bills can be considers riskless return but they still have reinvestment risk. If interest rate falls in the market then interest income will also fall down. Treasury bills are backed by U.S. government hence they don’t have default risk and liquidity risk.

c. Can you think of any asset that would be completely riskless? Could someone develop such an asset/ explain.

Answer: It is not possible to develop riskless assets. Only U.S treasury bills are default and liquidity risk free because they are backed by U.S. government however in real life it is not possible to construct any assets or portfolio which does not have any risk.

6-5

If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase more or less than that on a low-beta stock? Explain.

Answer: If investors’ aversion to risk increased then the risk premium on high-beta stock increase more than that on a low-beta stock. It is because the effect of the change in the risk aversion is stronger on more risky securities than in less riskier securities. Beside this, there is the positive relationship between risk aversion and the risk premium. If the risk aversion increases then the risk premium also goes up causing the slope of the security market line (SML) to become steeper. The steeper the Security market lines higher the required rate of return. Risk premium for stock x can be calculated as: Risk premium of market (RP

_{M}) multiply by beta of stock x (β_{x}). For example, Market risk premium (RP

_{M}) = 6%Beta for stock X = 0.7

Beta for stock Y = 1.4

Now, calculation of risk premium for stock X and Y.

Risk premium for stock X = Market risk premium X beta

= 6% X 0.7

= 4.2%

Risk premium for stock Y = Market risk premium X beta

= 6% X 1.4

= 8.4%

Again, let’s suppose investors’ risk aversion increase that leads market risk premium to increase from 6% to 8% and beta for those stock remain the same.

Risk premium for stock X = Market risk premium X beta

= 8% X 0.7

= 5.6%

Risk premium for stock Y = Market risk premium X beta

= 8% X 1.4

= 11.2%

The above example clearly shows that risk premium for stock Y which has higher beta increase more than stock X which has lower beta. Therefore, risk premium on a high-beta stock increase more than low beta stock when investors’ aversion to risk increase.

6-6

If a company’s beta were to double, would its expected return double?

Answer: No, expected return would not be doubled if company’s beta were to double. According to Security Market Line (SML) equation, Company’s expect return is Risk free return plus market risk premium (market risk – risk free return) times Company’s beta.

For example, Risk free return = 8%

Market risk premium = 2%

Current beta of company (β) = 0.4

Then Company’s expected return = RF + (r

_{m}– r_{RF}) β = 8% + 2% X 0.4

= 8.8%

Now support Company’s beta (β) doubled from 0.4 to 0.8

Then Company’s expected return = RF + (r

_{m}– r_{RF}) β = 8% + 2% X 0.8

= 9.6%

Therefore, expected return of the Company increase when beta of the company increase but it would not be double if Company’s beta double.

6-7

Is it possible to construct a portfolio of stocks which has an expected return equal to the risk-free rate?

Answer: It is only possible when the beta is zero but in the real world it is difficult to find an individual stock which has zero betas. Therefore, we can say that constructing a portfolio of stocks which has an expected return equal to the risk-free rate is impossible. A portfolio has two types of risk on it, first is diversifiable risk (unsystematic risk) and second is non diversifiable risk (systematic or market risk). Diversifiable risk can be eliminated by combining stocks which have negative correlation while market risk which is systematic risk cannot be eliminated. In real practice it is almost impossible to find out stocks which have negative correlation. When a portfolio has risk then its return should be higher than risk-free return. All kinds of portfolios have some unsystematic risk as well as systematic risk and hence it is impossible to construct a portfolio of stocks which has an expected return equal to risk- free rate.

References

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