# Money (Dollar) Weighted Question

Question: • On 1-Jan the Fund has a market value of \$100 million • During the period of 1-Jan to 30-Apr, the stocks in the fund showed a capital gain of \$10 million. • On 1-May, the stocks in the fund paid a total dividend of \$2 million. All dividends were reinvested in additional shares. • Because the fund’s performance had been exceptional, institutions invested an additional \$20 million in the fund on 1-May raising the assets under management to \$132 million. • On 31-Dec, the fund received total dividends of \$2.64 million. The fund’s market value on 31-Dec, not including the \$2.64 million in dividends was \$140 million Compute the Fund’s Money Weighted rate of return. Answer: A \$100 million initial investment followed by the \$2 million dividend reinvested and an additional \$20 million of new investment. (Occurring at the end of the first four month period). No cash flows in the second four month interval and \$142.64 million cash inflow in the third four month interval. My question: why is the dividend re-investment and additional new investment considered to be included in the first four month period, even though it occurs on the first day of the fifth month (or the second four month interval)? Why is it CF0 = -100, CF1 = -20, CF2, = 0, CF3 = 142.64 and not CF0 = -100, CF1 = 0, CF2 = -20, CF3 = 142.64? Any insight would be appreciated!

CF1 is at the end of 4 months CF2 at the end of 8 months CF3 at the end of 12 months. Dividend and additional investment happened at the end of first 4 months.

Because we are using end of period, not beginning of period. Your method would assume that the investment was made on 31st august. remember, MWR is just IRR, and you have to use equal length periods. Unless you want to use 365 periods, then 3 periods is close enough! Always remember to check that your BAII+ is in END mode, not BGN mode when working these out.

Think from the ‘ordinary’(End of period) and annuity due(Begin of period) point of view…how many periods do you want to discount it for… If you include it in CF2, you discount for 2 periods(8 months), but you want to discount only for 1 period(4 months).