You manage a $95 million Australian equity portfolio with a beta of 1.10. Over the next four months, the S&P/ASX200 index rises from 7100 to 7395, and the market generates a 0.8% dividend yield during this period. The risk-free interest rate is 2.5% per annum, continuously compounded. What is the new value of the portfolio after four months? Select the closest/best answer choice.[Fill in the blank]单项选择题
A
a. $99,400,000
B
b. $100,550,000
C
c. $100,098,735
D
d. $99,900,000

Question

You manage a $95 million Australian equity portfolio with a beta of 1.10. Over the next four months, the S&P/ASX200 index rises from 7100 to 7395, and the market generates a 0.8% dividend yield during this period. The risk-free interest rate is 2.5% per annum, continuously compounded. What is the new value of the portfolio after four months? Select the closest/best answer choice.[Fill in the blank]单项选择题

A

a. $99,400,000

B

b. $100,550,000

C

c. $100,098,735

D

d. $99,900,000

BlackTom AI · Accepted Answer

Use the CAPM relation for realized period returns: r_portfolio = r_f + beta*(r_market - r_f).

1) Compute the market total return over four months (price change + dividends).
- Price return = 7395/7100 − 1 = 0.04154929577 (4.1549296%).
- Dividend yield over period = 0.00800000000 (0.8%).
- Market total return r_m = 0.04154929577 + 0.008 = 0.04954929577 (4.9549296%).

2) Compute the four-month risk-free rate from the continuously compounded annual rate 2.5%:
- Period = 4/12 = 1/3 year.
- r_f(period) = e^{0.025*(1/3)} − 1 = e^{0.0083333333} − 1 ≈ 0.0083680080 (≈0.8368008%).

3) Apply CAPM to get the portfolio return for the period:
- Excess market return = r_m − r_f = 0.04954929577 − 0.0083680080 = 0.04118128777.
- Portfolio excess = beta * excess market = 1.10 * 0.04118128777 = 0.04529941655.
- Portfolio period return r_p = r_f + portfolio excess = 0.0083680080 + 0.04529941655 = 0.05366742455 (≈5.3667425%).

4) Apply this return to the $95,000,000 portfolio:
- New value = 95,000,000 * (1 + 0.05366742455) = 95,000,000 * 1.05366742455 ≈ $100,099,405.
Rounded to the nearest provided choice, this is essentially $100,098,735 (choice c). Small differences are due to rounding in intermediate steps.

Why other choices are incorrect:
- a. $99,400,000 and d. $99,900,000 are lower than the amount produced by a positive market movement and the portfolio’s beta > 1, so they understate the gain.
- b. $100,550,000 is noticeably higher than the CAPM-implied result and overstates the portfolio’s sensitivity.