Question

The following table represents yourcash inflows and outflows to the Efficient Minds Capital Emerging Market Growth Fund. As you can see, you panicked at the end of the first year by withdrawing 30,000 after seeing a 20% decline in your portfolio (i.e., you sold low). In year 2 you regained your confidence in Efficient Minds Capital by reinvesting 40,000 following the stellar 50% returns. You sat still in year 3 and then pulled out all of your money at the end of year 4.

Year	0	1	2	3	4
Beginning value		100,000	50,000	115,000	126,500
Gain (%)		-20%	+50%	+10%	+10%
Gain ($)		-20,000	+25,000	+11,500	+12,650
Inflow (+) or Outflow (-) from fund		-30,000	+40,000	0	-139,150
Ending value	100,000	50,000	115,000	126,500	0

1) What is the time-weighted return (i.e., how well did the Efficient Minds Capital fund manager do)? Express your answer in decimal notation on an annualized basis using the geometric average return.

2) Calculate the dollar-weighted return using MIRR and presuming your finance rate and reinvestment rate are both 10%. Express your answer in decimal notation. [Hint: remember, an inflow (+) to the fund is an outflow (-) from your pocket and vice-versa]

3)Efficient Minds Capital Agressive Growth fund had an average return of 22.09%, a standard deviation of 17.27% and a beta of 1.24. The risk free rate during the same period was 7.96%. What is the Sharpe (RVAR) ratio?

Answer 1

(1).

Calculating Time weighted return,

T0	100000
T1	80000
T2	75000
T3	126500
T4	139150

30000 withdrawal after T1 and 40000 deposit after T2.

In holding period H1, R1= (80000-100000)/100000 = -20%

In holding period H2, R2= (75000-80000+30000)/80000= 31.25%.

In holding period H3, R3= (126500-75000-40000)/75000= 15.33%.

In holding period H4, R4= (139150-126500)/126500= 10%.

So, Time weighted return= (1+R1)*(1+R2)*(1+R3)*(1+R4)-1= (1-0.2)*(1+0.3125)*(1+0.1533)*(1+0.1)-1= 33.21%.

(2).

Calculating dollar weighted return,

	T0	T1	T2	T3	T4
Investor cash flow	-100000	30000	-40000	0	139150
Ending balance	100000	50000	115000	126500	0

need to find using MIRR as instructed, MIRR=(FV(positive cash flows,reinvestment rate)/PV(negative cashflows,finance rate))^(1/n)-1; given that both reinvestment rate and finance rate is 10%, we get MIRR=7.71%.

So, dollar weighted return is 7.71%.

(3).

Given average return= 22.09%, standard deviation= 17.27%, beta=1.24, risk free rate= 7.96%.

So, Sharpe ratio= (expected return-risk free rate)/standard deviation= (22.09%-7.96%)/17.27%= 0.818