Question

The below table summarizes the respective daily returns from Dec. 10 2018 to Dec. 14 2018 for a large-cap portfolio, mid-cap portfolio, small-cap portfolio. Compute the respective 5-day holding period returns for three portfolios and explain their portfolio performances. Date Large-Cap Stocks Mid-Cap Stocks Small-Cap Stocks 12/10/2018, Monday -0.1% 0.2% 1.1% 12/11/2018, Tuesday 0.5% 0.1% -0.9% 12/12/2018, Wednesday 0.2% -0.4% 0.3% 12/13/2018, Thursday -0.1% -0.2% 1.2% 12/14/2018, Friday 0.9% 0.3% -0.2%

Answer 1

When daily returns are given, total holding period returns are calculated using the formula:

This can be understood as follows: Suppose you had invested $100 in the large cap stocks. Then, your return after respective days would be:

day 1: 100*(1 - 0.1%) =  99.9

day 2: 99.9*(1 + 0.5%) = 100*(1 - 0.1%)(1 + 0.5%) = 100.4... and so on.

(The -1 at the end of the formula is to remove the 1 added to all returns.)

So, using the formula and substituting values we get the holding period returns as:

Large cap:

or 1.40%

Mid cap:

or 0.00% (rounded off)

Small cap:

=1.49%