Question

the following information about the activity in two investment accounts: 3. You are given the following information about the Account B Fund value Account A Fund value before With- Date activity Deposit drawal 1/1/07 1,000 4/1/07 1,170 150 10/1/07 940 300 12/31/07 970 Date 1/1/07 8/1/07 12/31/07 before With- activity Deposit drawal 1,000 1,080 3X 1,595 -weighted (money-weighted) return for investment account A equals the During 2007, the dollar-weighted (money-wei time-weighted return for investment account B. Calculate X. (A) 146.00 (B) 150.33 (C) 154.67 (D) 158.33 (E) 162.67

Answer 1

Dollar weighted return can be calculated using IRR method or Modified Dietz method. For simplicity sake we will use modified dietz method here.

Rate of return =

(EMV – BMV - Ci)/(BMV + Wi* Ci)

where,

EMV = Ending Market Value,

BMV = Beginning Market Value,

Ci = cash flow occurring at time i, and

Wi is the weight is proportion of time between the point in time when the flow occurs and the end of the period i.e. ratio of the number of days from cash flow till the end of the period and the total number of days.

ROR = (970-1000-(+150-300)) / (1000 + (274/365*150 - 91/365*300)) =11.5628%

To calculate time weighted rate of returns we will calculate the return of each subperiod and then link the returns.

There are two sub-periods (01-01-07, 08-01-07) and (08-01-07, 12-31-07)

Return for sub period (01-01-07, 08-01-07) = (EMV - BMV ) / BMV = (1080 - 1000)/1000 = 8.00%

At 08-01-07, there is a deposit of 3X, hence the market value at the end of 08-01-07 is 1080+3X. This will be our BMV

EMV at 12-31-07 is given as 1595

Hence return for sub period (08-01-07, 12-31-07) = (1595 - (1080+3X) ) / (1080+3X)

Now we will link these two sub-period returns to calculate the Time Weighted Return (TWR) for the year

(1+ TWR for the year )= (1+Return for sub period (01-01-07, 08-01-07))*(1+return for sub period (08-01-07, 12-31-07))

= (1+8%) * (1+(1595 - (1080+3X) ) / (1080+3X) )

It is given that the DWR for Account A is equal to TWR for Account B

Hence

(1+11.5628%) = (1+8%) * (1+(1595 - (1080+3X) ) / (1080+3X) ) = (1+0.08) * ( (1080+3X) + 1595 - (1080+3X) ) / (1080+3X) )

= 1.08 * 1595/(1080+3X) = 1722.6 / (1080+3X)

(1080+3X) = 1722.6 / (1+11.5628%) =1544.063075

3X = 1544.063075 - 1080

Hence X = 154.68

Answer: The value of X is option C 154.67 (this is the closest to the answer we got. this may be because of rounding error)