Mar

7

Japanese geishaSP500 weekly returns 1/84-present were checked for mean and stdev:

mean 0.001671
stdev 0.023238

Random number generator was used to generate 100 simulated 36-year markets, with the same stdev (0.023238) but with a mean weekly return of zero. The means of all 100 simulated markets were ranked, and the highest one was found to be 0.001663.

So the probability that actual SP500 weekly returns averaged what it did - 0.001671 - by chance alone - was <1%.

Over the same period for Japan's Nikkei 225, the actual mean and stdev for weekly returns was:

mean 0.000455
stdev 0.029022

Using the same method as for SP500 simulation, the random number generator was used to generate 100 simulated 36-year markets, with the same stdev (0.029022) but again a mean weekly return of zero. The means of all 100 simulated markets were ranked, and the highest one was found to be 0.00174. The actual mean of 0.000455 ranked 30th out of 100 simulated weeks. Japanese stock market drift had a 30% probability of occurring by chance alone.

If upward drift was the result of return for risk, why didn't it occur in Japan?

A friend suggested evaluating drift after adjusting for risk-free return (in this case, 30 day t-bill rates available as concurrent alternative to SP500 index investing). Weekly 30-day t-bill yield data from FOMC* (which uses annualized yield) was converted to weekly yield, and SP500 weekly returns were converted to "risk free return" by subtracting the weekly 30 day yield.

SP500 mean weekly returns (1954-present), and SP500 weekly "risk free" were compared to zero with t-test:

One-Sample T: wk ret, "risk free"

Test of mu = 0 vs not = 0

Variable        N         Mean      StDev     SE Mean          95% CI            T          P
wk ret       2929  0.00152  0.0210  0.0003  ( 0.0007, 0.0022)  3.93  0.000
"risk free"  2930  0.00055  0.0210  0.0003  (-0.0002, 0.0013)  1.43  0.152

Subtracting risk free rate of return dropped the return for SP500 by about 2/3, after which drift is no longer significantly different than
zero.

Jordan Low comments:

Are all dividends included? Perhaps it is because Japanese hold stocks for different reasons? I was in Tokyo when JAL went under and some people were happy to pay 1 yen to be a shareholder to get a certain number of tickets for half price a year.


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