You begin to track the performance of your 401k plan. Assuming you started with

Question

You begin to track the performance of your 401k plan. Assuming you started with $50,000 which you put in a stock fund that tracked the S&P 500. At the end of year 1 the fund returned +10% and at the end of year 2, the fund suffered a 10% loss.

Answer the following questions assuming you made no contributions or withdrawals during this period:

a) How much do you have in your account at the end of year 2?

b) What is the total return over the 2-year period?

c) What is the average annualized geometric return over the period?

d) What is the arithmetic average annual return over the period?

e) Which approach arithmetic or geometric average return is more indicative of your performance?

f)    Now assume that at the end of year-1 after earning a 10% return, you sold $5,000 of the stock fund (which represents the dollar amount of the 10% gain in year-1) and put the proceeds in cash. In year-2 the stock fund suffered a 10% loss of the remaining $50,000 leaving you with $45,000 plus the $5,000 in cash gives you back your original $50,000. Calculate your return over the two year period.

Explanation / Answer

a) Since we started with $50,000 and return is +10% in year 1. At the end of year 1, total value is 50,000*1.1 = $55,000 and then in year 2, return is -10%, so balance at the end of year 2 is $55,000*(1-10%) = $49,500

b) Total return over 2 year period is -500/50,000 = -1%

c) Let average annualized geomatric return is r

then, (1+r%)^2 = 0.99

r = -0.50125%

d) Arithematic average return is -0.5% (-1%/2)

e) Geomatric return is more indicative in finance as the return on second period is dependend on the return on first period.

f) Return over 2 year period now is 0% (we started with $50,000 and have $50,000 at tne end of 2 years)

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