Fight Finance

Question 917  Macaulay duration, duration

Which of the following statements about Macaulay duration is NOT correct? The Macaulay duration:

(a) Is the weighted average time that an asset’s cash flows are received.

(b) Is measured in units of time, usually years.

(c) Of a zero-coupon bond is equal to the bond’s maturity.

(d) Of a fixed-coupon-paying bond will be more than the bond’s maturity.

(e) Of a portfolio is an arithmetic average of the Macaulay durations of the assets in the portfolio, weighted by their prices.

Question 997  duration

Which of the following assets would have the shortest duration?

(a) Consumer staple stocks with high payout ratios such as shares in supermarkets.

(b) Fast-growing technology stocks with low payout ratios such as shares in software companies.

(c) Fixed coupon 3 year government bonds that were just issued and pay semi-annual coupons.

(d) Floating coupon 3 year corporate bonds that were just issued and pay semi-annual coupons.

(e) 90 day certificate of deposit.

Question 996  duration, CAPM

Assume that the market portfolio has a duration of 15 years and an individual stock has a duration of 20 years.

What can you say about the stock's (single factor CAPM) beta with respect to the market portfolio? The stock's beta is likely to be:

(a) Higher than the market portfolio's beta.

(b) Lower than the market portfolio's beta.

(c) Equal to the market portfolio's beta.

(d) There's not enough information to answer the question.

Question 999  duration, duration of a perpetuity with growth, CAPM, DDM

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the Macaulay duration of the stock now?

(a) 13.75 years

(b) 14.333333 years

(c) 19.545455 years

(d) 35 years

(e) Infinity

Question 1000  duration, duration of a perpetuity with growth, needs refinement

An unlevered firm cuts its dividends and re-invests in zero-NPV projects with the same risk as its existing projects. This decreases the dividend yield, but increases the firm's equity's dividend growth rate and duration, while its total required return on equity remains unchanged. The equity can be valued as a perpetuity and the duration of a perpetuity is given below:

###D_\text{Macaulay} = \dfrac{1+r}{r-g}###

What will be the effect on the stock's CAPM beta? Assume that there's no change in the risk free rate or market risk premium. The company's equity beta will:

(a) Increase.

(b) Decrease.

(c) Remain unchanged.

(d) Not enough information is provided to answer the question.