# Asset Allocation In The Eyes Of The Kelly Strategy

First, let me introduce myself. I am a middle-aged guy who has a stable job, a good income, and am not financially stressed. I have thirty more years of working life before retirement. Through my work, I have a self-directed 410K account. In addition, I have been a part time trader for many years and mostly trade options. "Risk" is virtually my middle name. Now, I am facing a simple asset allocation question for my 410K account. If I have been given the opportunity to either invest in S&P 500 ETF (NYSEARCA:SPY) or in cash, what should be my ratio for these two asset classes?

The answer is simple. If I take any risk assessment questionnaire, my risk tolerance level will be off-the-charts, so I should be 100% in S&P. Easy, right?

Not so fast. First, Mr. Market really doesn't care who I am and what I care; he has his own rhythm. The only decision I make that may have a causal effect on the portfolio performance is how soon I will need the money, or how often I rebalance my portfolio. My simple problem can now be rephrased as:

What is the most effective way to increase my bankroll using SPY as the betting vehicle?

This problem has been thoroughly addressed by the Kelly Strategy (for readers unfamiliar with it, I recommend "Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street" by William Poundstone). In brief, the Kelly Strategy stated that the optimal betting size is calculated as:

f = p-q/b

where f is the percentage of the bankroll, p is the probability of winning, q is the probability of losing, and b is the ratio of size between expected winning and losing bets.

Now we can do some calculation on SPY. I downloaded from S&P the excel sheet of the monthly SPY prices from 1987-2012, which provides the rolling 1,3,6 months 1,2,3,5,10 years, and 1-month and 1-year total return including dividend. After a simple excel sheet calculation on the Kelly ratio, here is the table:

 SPY win percentage loss percentage win size loss size Kelly ratio 1Month 62.5% 37.5% 3.3% -3.6% 21.5% 3Month 65.8% 34.2% 6.2% -6.0% 32.3% 6Month 70.4% 29.6% 6.2% -6.0% 41.5% 1 year 75.1% 24.9% 15.8% -15.5% 50.7% 2 year 77.6% 22.4% 29.3% -22.6% 60.4% 3 year 76.4% 23.6% 43.2% -21.0% 64.9% 5 year 72.4% 27.6% 77.4% -11.7% 68.3% 10 year 90.7% 9.3% 171.4% -23.4% 89.4% 1 Month (total return) 63.9% 36.1% 3.3% -3.5% 25.6% 1 year (total return) 80.1% 19.9% 17.9% -16.7% 61.5%
Click to enlarge

As an example, the 1 month SPY wins 62.5%, and loses 37.5%, the average size of win is 3.3%, and the average size of loss is 3.6%. In this case, the optimal betting based on Kelly ratio is 21.5% of the bankroll.

There are quite a few interesting points here:

(1) In all series, it is not recommended to bet the entire stake on SPY, even for the very long term (10 year).

(2) Kelly ratio indicated that if monthly rebalancing is used, one should bet a very small portion (21.5%) of the bankroll. This is in alignment with a conservative portfolio for people who are close to the retirement age. But, monthly rebalancing seems not to be a good growth strategy.

(3) Based on the total return of SPY, and rebalancing yearly, one should bet the golden 60/40 ratio on SPY (or more precisely 61.5/38.5). I am not recommending to keep the rest 40% all in cash, but it would be ideal to keep them in an asset class that has zero correlation with SPY.

For readers who have access to the historical SPY with longer duration, it will be interesting to find out if the same Kelly ratio holds true.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.