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The stocks of CK Tan's, Robertson's, and Tamashimaya are held by the hedge fund SSK. They hold an equally weighted portfolio. The end-of month prices of the stock during five months this year is given as

enter image description here

a) Calculate the simple monthly returns of the three stocks. Calculate the log returns.
b) Using answers of a), what is the return of the hedge fund SSK for each month?
c) Calculate the five-month returns of the three stocks and the hedge fund, respectively. Discuss which returns you would add up.

Would appreciate if someone could verify my workings as I'm unsure.
Answer:

a) enter image description here

b)
June returns = (10%+12%+4%)/3 = 8.67%
July returns = -17.69%
August returns = -2.59%

c) For the 3 stocks, the monthly log returns are summed to derive the 5-month returns. The hedge fun returns are calculated by summing the log values of b)

CK Tan's = 9.53% - 20.07% + 10.54% + 18.23% = 18.23%
Robertson's = 27.76%
Takashimaya = -91.63%
Hedge fund = ln(8.67%) + ln(-17.69%) + ln(-2.59%) (This is the part I doubt the most)
Hedge fund = ln(8.67%- 17.69%- 2.59%)
Hedge fund = 5.98%

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You are missing the weights for b and c. Since it does not explicitly state that the portfolio is rebalanced each month, it would not be correct to use 1/3 to calculate monthly returns.

If you insist using monthly rebalanced equally weighted portfolio, then use simple returns to calculate the Hedge Fund return for each month, convert to log space, and then sum them up. Portfolio additive vs Time additive

Be careful.

Also, your August return is actually September's return, if you assume monthly rebalanced equal weighted portfolio.

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  • $\begingroup$ Hi there, appreciate the response! Can you perhaps elaborate on that? As it's an equally weighted portfolio, I simply divided their total returns by 3 for b. For c, since it's returns across different periods, how do the weights impact returns? $\endgroup$
    – SMLJKNN
    Commented Aug 31, 2019 at 8:13
  • $\begingroup$ elaborated further. overall, this is a very badly formulated set of questions :) $\endgroup$
    – AK88
    Commented Aug 31, 2019 at 22:38

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