11.36. Assume that the typical day-to-day noise (standard deviation) is about 10
ID: 2730460 • Letter: 1
Question
11.36. Assume that the typical day-to-day noise (standard deviation) is about 100 basis points. Assume that you have the kind of stock-picking ability that earns you an extra 400 basis points per annum. Assume no transaction costs. Ignore compounding and assume that your rate of return is the sum of re-turns over trading days. Assume there are 252 trading days per year. 1.With only 1 day of performance, how much extra do you expect to earn per day? 2. How bad is your noise over 1 day? 3. What is your expected T-statistic (the excess mean divided by the standard deviation)? 4. With 252 trading days of performance, how much extra do you expect to earn per annum? 5. How bad is your noise over 252 days? 6. What is your expected T-statistic now? 7. Work out how many years you would expect to wait before you would obtain statistically signif icant evidence to prove that you have a positive ability to pick stocks.
Explanation / Answer
Q. 1) Extra that you expect to earn per day :-
Per month extra earn = 4 / 12 = 0.33 % [ 400 Basis point = 400 / 100 = 4 %]
Extra that you expect to earn per day = 0.33 / 30 [ 1 Month = 30 Days]
= 0.01 %
Q. 2) Bad noise over 1 day:-
Per month bad noise = 1 / 12 =0.0833
[ 100 Basis Point = 100 / 100 = 1 %. Assuming 100 basis point given in the question is per annum as the extra earnings of 4 % given in the question is also of per annum.]
Bad noise over 1 day = 0.0833 / 30 = 0.003 % (approx) [ 1 Month = 30 Days]
Q. 3) Extra T-statistics = 0.01 / 0.003 = 3.33 %
Q. 4) Extra expect to earn per annum with 252 trading days:-
Per day extra earn = 0.01 % (Calculated in Question 1)
Thus, Extra expect to earn per annum with 252 trading days = 0.01 * 252
= 2.52 %
Q. 5) Bad noise over 252 Days:-
Per day bad noise = 0.003 %
Thus, Bad noise over 252 Days = 0.003 * 252
= 0.756 %
Q. 6) Expected T-statistics now = 2.52 / 0.756 = 3.33 %
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