Question

Q1. J. Kasoma invested K10 000 on 1st January with X Funds. During the 6 six months the Fund had capital gains of K1 000. On July 1st the fund paid a K200 dividend, which he immediately reinvested. On July 1st he invested another K5 000. The fund value at the end of the year is K16 000 and a dividend of K200 is paid.

A. Calculate the time-weighted rate of return.                                                                [8 Marks]

B. Explain the relationship of your answer in part A to the first six months yield.               [4 Marks]

C. Why is the money-weighted rate of return not ideal as a portfolio manager’s performance measure?                                                                                                                              [4 Marks]

D. Explain the advantage of using the time weighted rate of return.                                     [4 Marks]

Q2. J. Miti has a portfolio worth K9 000. He then inherits shares of Alick Ltd worth K1 000. He seeks your guidance regarding whether he should keep his inheritance.

	Expected Returns	Standard Deviation	Correlation of original portfolio and Alick Ltd
Original Portfolio	0.67%	2.37%	0.4
Alick Ltd	1.25%	2.95%

A. Adding his inheritance to his original portfolio, calculate his new portfolio’s expected return.                                                                                                                                                                    [4 Marks]

B. Calculate the new portfolio’s standard deviation.                                                                [6 Marks]

C. Calculate the Coefficient of Variation [CV] of the new portfolio.                           [4 Marks]

D. Should Mr. Miti keep the newly acquired Alick Ltd shares? Justify your reason using your vast investment analysis expertise.                                                                                          [6 Marks]

                                                                                                                          [TOTAL: 40 MARKS]

Answer 1

A. Calculate the time-weighted rate of return.

Return for the first period, from 1st January to July 1st   would be calculated as

Investment = 10000

Capital gain = 1000

Dividend = 200

Value of the X funds on 1 July = 10000+1000+200 = 11200

Return = (11200-10000)/10000 = 12%

Return for the second period, from 1st July to end of the year   would be calculated as

Reinvestment amount = 5000

Value of the fund on 1st July = 11200+5000 = 16200

Value end of the year = 16200

Return = 16200-16200/16200 = 0%

Time-weighted rate of return = (1+12%)*(1+0%)-1 = 12%

B. Explain the relationship of your answer in part A to the first six months yield.

Return after six month = 12 %

Time-weighted rate of return = 12 %

Both are equal because Fund value 16200 after six month because of capital gain, dividend & reinvestment after this end of the year the fund valued 16200.

D. Explain the advantage of using the time weighted rate of return.

Time-weighted rate of return useful because inflows and outflows of cash in the fund impact the growth rates and time-weighted rate of return eliminate that distorting effect on the rate.

C. Why is the money-weighted rate of return not ideal as a portfolio manager’s performance measure?

We noticed that with an inflow of 5000 the time-weighted rate of return and return after six months becomes equal. The inflow and outflow of the cash sometimes create such situation where maybe portfolio managers have performed well but the money-weighted rate of return will not show that.