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I am trying to understand Sharpe Ratio and I have tried to calculate it and compare it with Sharpe Ratio value from Yahoo Finance.

I took daily closing prices for SPY from February 1st, 2018 till January 29, 2021 (inclusive).

Date
2018-02-01    281.579987
2018-02-02    275.450012
2018-02-05    263.929993
2018-02-06    269.130005
2018-02-07    267.670013
                 ...    
2021-01-25    384.390015
2021-01-26    383.790009
2021-01-27    374.410004
2021-01-28    377.630005
2021-01-29    370.070007

Calculated daily change:

Date
2018-02-02   -0.021770
2018-02-05   -0.041823
2018-02-06    0.019702
2018-02-07   -0.005425
2018-02-08   -0.037509
                ...   
2021-01-25    0.003944
2021-01-26   -0.001561
2021-01-27   -0.024440
2021-01-28    0.008600
2021-01-29   -0.020020

Mean value of daily change values:

0.0004691536096486628

The standard deviation of daily change values:

0.014525375524599708

Calculated Sharpe Ratio according to the formula: 'square root of 252' x 'Mean value of daily change values' / 'standard deviation of daily change values':

0.512729096352712

According to Yahoo Finance, the 3-year Sharpe ratio for SPY is 0.72, not 0.51.

Question 1. Why I am getting a different value other than Yahoo Finance?

Question 2. As I understood the higher Sharpe Ratio, the better. Why do not investors just calculate Sharpe Ratio for all stocks and invest in stocks with the highest Sharpe Ratio?

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  • I don't know the answer but Yahoo is notorious for providing bad data. See if you can find another source for comparison and perhaps it will align with your calculations. If it aligns with Yahoo's data then maybe your analysis is off. – Bob Baerker Feb 1 at 16:44
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All the Sharpe Ratio measures is how much excess return (meaning return above a "risk-free" investment like US Treasury Bonds) you get for each "unit" of risk. In this case a unit is 1 standard deviation. So portfolios with a higher sharpe ratio use risk more effectively.

Why I am getting a different value other than Yahoo Finance?

Most likely because you're calculating return differently. The return in the sharpe ratio calculation is the return of the portfolio over that period over a risk-free return (in reality you can use 0 as a "benchmark" risk-free return, but most likely Yahoo is using a risk-free rate of some sort). So you would take the geometric average of returns (not arithmetic) and subtract a "risk-free" rate at the end. There are multiple articles in the internet on how to calculate Sharpe Ratio.

As I understood the higher Sharpe Ratio, the better. Why do not investors just calculate Sharpe Ratio for all stocks and invest in stocks with the highest stocks?

This is only true when comparing investments of similar risk. A bond portfolio may have a much higher sharpe ratio than a small-cap equity portfolio because it has much lower risk. For example, a bond portfolio that has an excess return of 4% with a risk of 2% would have a sharpe ratio of 2, while a small-cap equity portfolio may have an excess return of 10% but a risk of 8%, for a sharpe ratio of 1.25. So if you are a risk-averse investor, the bond portfolio may be a better use of risk, but a risky investor may want the portfolio with a higher absolute expected return (i.e. willing to risk more for the possibility of earning more).

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