Question

Deposits of $1000 are made into an investment fund at time 0 and 1. The fund balance is $1200 at time 1 and $2200 at time 2.

(a) Compute the annual effective yield rate computed by a dollar-weighted method.

(b) Compute the annual effective yield rate which is equivalent to that pro- duced by a time-weighted method.

Answer 1

a) Say , Rd is the dollar weighted return

Formula for dollar weighted return: Fund Value at time t= Initial Fund+ Present Value of all other fund deposited after at discount of Rd

So, 2200/(1+Rd)^2=1000+1000/(1+Rd)

by solving above equation Rd= 6.525%

So, dollar weighted return=6.525%

b) After time 1 realized return=(1200-1000)/1000 i.e 20%, and fund value becomes 2200 at time 1

So, from time 1 to 2 return generated= (2200-2200)/2200 i.e. 0%

So, Time weighted return= (1+20%)*(1+0%)-1 i.e. 20% in time 2. SO, yearly annual yield is 20%/2 or 10%.