Looking for the Best SPY/Cash Rebalancing Threshold in Terms of Sharpe Ratio

This is a study on the effects of rebalanced threshold on mean daily reutns and the standard deviation. 

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Fed Funds Rate:%

The daily rate: %, which is the Fed funds rate divided by 365.

SPY Ratio:%
Cash Catio:%

Looking for the Best SPY/Cash Rebalancing Threshold in Terms of Sharpe Ratio

In this article, I have found that some the best SPY/Cash rebalanced portfolio are the following:

• The mean return divided by the standard deviation of 0.04089 from a 60% SPY/40% cash portfolio with a rebalancing threshold of 14.8%.
• The mean return divided by the standard deviation of 0.04034 from a 50% SPY/50% cash portfolio with a rebalancing threshold of 17.4%.
• The mean return divided by the standard deviation of 0.04038 from a 50% SPY/50% cash portfolio with a rebalancing threshold of 28.1%.
• The mean return divided by the standard deviation of 0.04103 from a 40% SPY/60% cash portfolio with a rebalancing threshold of 30.4%.
• The mean return divided by the standard deviation of 0.04161 from a 30% SPY/70% cash portfolio with a rebalancing threshold of 30.4%.
• The mean return divided by the standard deviation of 0.04210 from a 20% SPY/80% cash portfolio with a rebalancing threshold of 27.1%.
• The mean return divided by the standard deviation of 0.04238 from a 10% SPY/80% cash portfolio with a rebalancing threshold of 18.2%.

And I want to test each of them to see if after apllying the risk free rate they are still the best. The way I apply the risk free rate is to subtract their mean daily return by the daily interest rate which is obtained by dividing the Fed funds rate by 252 since there are on average 252 trading days per year.

60% SPY/40% cash portfolio with a rebalancing threshold of 14.8%

The best rebalancing threshold is still 14.8%.

50% SPY/50% cash portfolio with a rebalancing threshold of 17.4% and 28.1%

Both 17.4% and 28.1% could be a very good threshold for SPY/Cash rebalancing.

40% SPY/60% cash portfolio with a rebalancing threshold of 30.4%

The best rebalancing threshold is still 30.4%.

30% SPY/70% cash portfolio with a rebalancing threshold of 30.4%

The best rebalancing threshold is still 30.4%.

20% SPY/80% cash portfolio with a rebalancing threshold of 27.1%

The best rebalancing threshold is still 27.1%.

10% SPY/90% cash portfolio with a rebalancing threshold of 18.2%

The best rebalancing threshold is still 18.2%.

Conclusion

• With the Fed funds rate being 1.75%, the best strategy is 90% cash with 10% SPY and rebalance with a threshold of 18.3%.
• A 100% SPY portfolio has a Sharpe ratio of 0.03695.
• When cash percentage is at 90%, the best Shape ratio is 0.04238 when the Fed funds rate is 0% and it drops to 0.04193 when the Fed funds rate is increased to 1.75%. This means cash does not add excess value to the portfolio. Same thing happens to high cash percentage portfolio.
• This reflects the point about why Sharpe ratio takes the risk free rate into consideration in this article.