Question

Arthur buys $1,500 worth of stock. Six months later, the value of the stock has risen to $1,700 and Arthur buys another $1,000 worth of stock. After another eight months, Arthur's holdings are worth $2,300 and he sells off $800 of them. Ten months later, Arthur finds that his stock has a value of $1,600.

(a)

Compute the annual time-weighted yield rate of the stock over the two-year period. (Round your answer to two decimal places.)

(b)

Compute the annual dollar-weighted yield for Arthur over the two-year period. (Round your answer to two decimal places.)

Answer 1

a). Annual time weighted return (Rtwr) = [(rt1)*(t2)*(rt3)*.....*(rtn)]^(1/n) -1 where

rtn = return in time period n and n is the number of time periods

Time T0 = 0: Value v0 = 1,500

Time T1 = 6 months: Value v1 = 1,700 (Buys 1,000 worth of stock, so v1' = 1,700 + 1,000 = 2,700)

Time T2 = 14 months: Value v2 = 2,300 (Sells off 800 worth of stock, so v2' = 2,300 - 800 = 1,500)

Time T3 = 24 months: Value v3 = 1,600

rt1 = (v1/v0) = (1,700/1,500)

rt2 = (v2/v1') = (2,300/2,700)

rt3 = (v3/v2') = (1,600/1,500)

Rtwr = [(1,700/1.500)*(2,300/2,700)*(1,600/1,500)]^0.5 -1 = 1.48%

b). Dollar weighted return (Rdwr) is simply the IRR of the cash flows (CF).

If IRR is r then considering only interim cash flows, starting and ending values, we have

1,500*(1+r)^2 + 1,000*(1+r)^(18/12) - 800*(1+r)^(10/12) = 1,600

Solving for r, it comes out to be approx. -2.64%