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The Sharpe Ratio is a measure for calculating risk-adjusted return, and is the industry standard for such calculations. It was developed by Nobel laureate William F. Sharpe. Instead of just looking at the total return of a particular stock or ETF, the Sharpe Ratio also looks at how volatile the stock or ETF has been. The concept is to try to get as high of a total return as possible with as little volatility as possible. So the higher the Sharpe ratio, the better.
The standard formula for the Sharpe Ratio is:
(Average return - Risk-free rate of return)/Standard deviation of average return
The idea behind subtracting the risk-free rate of return was to measure risk taking. An ETF engaging in 'zero risk' investment, such as the purchase of U.S. Treasury bills, for which the expected return is the risk-free rate, has a Sharpe ratio of exactly zero.
Sharpe Ratio calculations tend to vary, for several reasons:
We calculate our own Sharpe Ratios for all ETFs. Our calculations are done in the following manner:
So, if you are looking at an older ETF, like IVE, the S&P 500 Value ETF, with an inception date of 05/22/2000, the Sharpe Ratio is 0.4638. IVE has been through two major market crashes (in 2002/2003 and 2008/2009), so it has a pretty low Sharpe Ratio during it's lifetime. But so too does SPY, an ETF that tracks the S&P 500 Index. SPY's Sharpe Ratio during the exact same time period is 0.4814.
A market crash obviously can have a significant impact on an ETF's Sharpe Ratio, because i) the average return of the ETF goes way down due to the market crash; and ii) the standard deviation of the return goes up due to the volatility. Because lifetime Sharpe ratios vary dramatically based on when the ETF was launched, it is important to only use the Sharpe Ratio to compare one ETF to the market (SPY) or another benchmark during the same time frame; absolute values are not important.
We know that we just said there is no real "target" Sharpe Ratio. But it is only natural to think: "what is a good Sharpe Ratio"? If you want to get a feel for Sharpe Ratios over long time periods, here are some examples:
Note that the Sharpe Ratio probably tends to have a bias towards bonds. AGG's Sharpe Ratio compared to SPY's Sharpe Ratio is significantly higher, despite the enormous difference in total returns. The Sharpe Ratio is designed to reward "slow and steady" returns, which bonds have had in recent years. Yet few people would advocate that long-term investors should have an investment portfolio made up strictly of bonds.
Step 1 - Build a table showing average returns by month, during the entire lifetime of the ETF (from inception until today):
| Year | Month | Opening Price | Closing Price | Gain (loss) | Dividend | Total Gain (loss) | Gain (loss) % |
|---|---|---|---|---|---|---|---|
| 2015 | 2 | $39.98 | $40.21 | $0.23 | $0.00 | $0.23 | 0.0058 |
| 2015 | 3 | $40.21 | $40.38 | $0.17 | $0.14 | $0.31 | 0.0076 |
| 2015 | 4 | $40.38 | $39.37 | $-1.01 | $0.00 | $-1.01 | -0.0250 |
| 2015 | 5 | $39.37 | $39.57 | $0.20 | $0.00 | $0.20 | 0.0051 |
| 2015 | 6 | $39.57 | $40.30 | $0.73 | $0.16 | $0.89 | 0.0224 |
| 2015 | 7 | $40.30 | $40.47 | $0.17 | $0.00 | $0.17 | 0.0042 |
| 2015 | 8 | $40.47 | $38.48 | $-1.99 | $0.00 | $-1.99 | -0.0491 |
| 2015 | 9 | $38.48 | $37.95 | $-0.53 | $0.18 | $-0.35 | -0.0090 |
| 2015 | 10 | $37.95 | $40.99 | $3.04 | $0.00 | $3.04 | 0.0801 |
| 2015 | 11 | $40.99 | $41.87 | $0.88 | $0.00 | $0.88 | 0.0215 |
| 2015 | 12 | $41.87 | $40.21 | $-1.66 | $0.25 | $-1.41 | -0.0336 |
| 2016 | 1 | $40.21 | $39.72 | $-0.49 | $0.00 | $-0.49 | -0.0122 |
| 2016 | 2 | $39.72 | $41.23 | $1.51 | $0.00 | $1.51 | 0.0380 |
| 2016 | 3 | $41.23 | $43.53 | $2.30 | $0.16 | $2.46 | 0.0596 |
| 2016 | 4 | $43.53 | $43.49 | $-0.04 | $0.00 | $-0.04 | -0.0009 |
| 2016 | 5 | $43.49 | $44.82 | $1.33 | $0.00 | $1.33 | 0.0306 |
| 2016 | 6 | $44.82 | $46.98 | $2.16 | $0.15 | $2.31 | 0.0515 |
| 2016 | 7 | $46.98 | $47.74 | $0.76 | $0.00 | $0.76 | 0.0162 |
| 2016 | 8 | $47.74 | $47.56 | $-0.18 | $0.00 | $-0.18 | -0.0038 |
| 2016 | 9 | $47.56 | $47.77 | $0.21 | $0.16 | $0.37 | 0.0078 |
| 2016 | 10 | $47.77 | $47.02 | $-0.75 | $0.00 | $-0.75 | -0.0157 |
| 2016 | 11 | $47.02 | $51.42 | $4.40 | $0.00 | $4.40 | 0.0936 |
| 2016 | 12 | $51.42 | $53.74 | $2.32 | $0.26 | $2.58 | 0.0502 |
| 2017 | 1 | $53.74 | $52.67 | $-1.07 | $0.00 | $-1.07 | -0.0199 |
| 2017 | 2 | $52.67 | $53.45 | $0.78 | $0.00 | $0.78 | 0.0148 |
| 2017 | 3 | $53.45 | $53.12 | $-0.33 | $0.16 | $-0.17 | -0.0031 |
| 2017 | 4 | $53.12 | $54.22 | $1.10 | $0.00 | $1.10 | 0.0207 |
| 2017 | 5 | $54.22 | $53.32 | $-0.90 | $0.00 | $-0.90 | -0.0166 |
| 2017 | 6 | $53.32 | $54.48 | $1.16 | $0.23 | $1.39 | 0.0261 |
| 2017 | 7 | $54.48 | $55.31 | $0.83 | $0.00 | $0.83 | 0.0152 |
| 2017 | 8 | $55.31 | $54.07 | $-1.24 | $0.00 | $-1.24 | -0.0224 |
| 2017 | 9 | $54.07 | $56.07 | $2.00 | $0.28 | $2.28 | 0.0421 |
| 2017 | 10 | $56.07 | $56.08 | $0.01 | $0.00 | $0.01 | 0.0002 |
| 2017 | 11 | $56.08 | $57.89 | $1.81 | $0.00 | $1.81 | 0.0323 |
| 2017 | 12 | $57.89 | $55.19 | $-2.70 | $0.34 | $-2.36 | -0.0407 |
| 2018 | 1 | $55.19 | $55.23 | $0.04 | $0.00 | $0.04 | 0.0007 |
| 2018 | 2 | $55.23 | $52.55 | $-2.68 | $0.00 | $-2.68 | -0.0485 |
| 2018 | 3 | $52.55 | $53.63 | $1.08 | $0.16 | $1.24 | 0.0235 |
| 2018 | 4 | $53.63 | $54.30 | $0.67 | $0.00 | $0.67 | 0.0125 |
| 2018 | 5 | $54.30 | $56.29 | $1.99 | $0.00 | $1.99 | 0.0366 |
| 2018 | 6 | $56.29 | $57.15 | $0.86 | $0.30 | $1.16 | 0.0206 |
| 2018 | 7 | $57.15 | $58.44 | $1.29 | $0.00 | $1.29 | 0.0226 |
| 2018 | 8 | $58.44 | $59.38 | $0.94 | $0.00 | $0.94 | 0.0161 |
| 2018 | 9 | $59.38 | $58.88 | $-0.50 | $0.23 | $-0.27 | -0.0045 |
| 2018 | 10 | $58.88 | $55.64 | $-3.25 | $0.00 | $-3.25 | -0.0551 |
| 2018 | 11 | $55.64 | $58.87 | $3.24 | $0.00 | $3.24 | 0.0581 |
| 2018 | 12 | $58.87 | $53.83 | $-5.05 | $0.38 | $-4.67 | -0.0793 |
| 2019 | 1 | $53.83 | $57.50 | $3.68 | $0.00 | $3.68 | 0.0683 |
| 2019 | 2 | $57.50 | $59.52 | $2.02 | $0.00 | $2.02 | 0.0351 |
| 2019 | 3 | $59.52 | $58.25 | $-1.27 | $0.19 | $-1.08 | -0.0181 |
| 2019 | 4 | $58.25 | $59.69 | $1.44 | $0.00 | $1.44 | 0.0247 |
| 2019 | 5 | $59.69 | $57.17 | $-2.52 | $0.00 | $-2.52 | -0.0422 |
| 2019 | 6 | $57.17 | $59.65 | $2.48 | $0.36 | $2.84 | 0.0496 |
| 2019 | 7 | $59.65 | $59.36 | $-0.29 | $0.00 | $-0.29 | -0.0049 |
| 2019 | 8 | $59.36 | $57.47 | $-1.89 | $0.00 | $-1.89 | -0.0318 |
| 2019 | 9 | $57.47 | $59.36 | $1.89 | $0.30 | $2.19 | 0.0381 |
| 2019 | 10 | $59.36 | $61.02 | $1.66 | $0.00 | $1.66 | 0.0280 |
| 2019 | 11 | $61.02 | $60.73 | $-0.29 | $0.00 | $-0.29 | -0.0048 |
| 2019 | 12 | $60.73 | $61.79 | $1.06 | $0.41 | $1.47 | 0.0242 |
| 2020 | 1 | $61.79 | $60.17 | $-1.62 | $0.00 | $-1.62 | -0.0262 |
| 2020 | 2 | $60.17 | $53.96 | $-6.21 | $0.00 | $-6.21 | -0.1032 |
| 2020 | 3 | $53.96 | $46.23 | $-7.73 | $0.28 | $-7.45 | -0.1381 |
| 2020 | 4 | $46.23 | $48.47 | $2.24 | $0.00 | $2.24 | 0.0485 |
| 2020 | 5 | $48.47 | $49.68 | $1.21 | $0.00 | $1.21 | 0.0250 |
| 2020 | 6 | $49.68 | $48.48 | $-1.20 | $0.29 | $-0.91 | -0.0183 |
| 2020 | 7 | $48.48 | $48.18 | $-0.30 | $0.00 | $-0.30 | -0.0063 |
| 2020 | 8 | $48.18 | $0.00 | $-48.18 | $0.00 | $-48.18 | -1.0000 |
| 2020 | 9 | $0.00 | $47.15 | $47.15 | $0.23 | $47.37 | 0.0000 |
| 2020 | 10 | $47.15 | $49.30 | $2.15 | $0.00 | $2.15 | 0.0457 |
| 2020 | 11 | $49.30 | $55.03 | $5.73 | $0.00 | $5.73 | 0.1162 |
| 2020 | 12 | $55.03 | $57.42 | $2.39 | $0.42 | $2.81 | 0.0511 |
| 2021 | 1 | $57.42 | $57.41 | $-0.01 | $0.00 | $-0.01 | -0.0002 |
| 2021 | 2 | $57.41 | $62.00 | $4.59 | $0.00 | $4.59 | 0.0800 |
| 2021 | 3 | $62.00 | $65.42 | $3.42 | $0.23 | $3.65 | 0.0588 |
| 2021 | 4 | $65.42 | $66.18 | $0.76 | $0.00 | $0.76 | 0.0116 |
| 2021 | 5 | $66.18 | $67.07 | $0.89 | $0.00 | $0.89 | 0.0134 |
| 2021 | 6 | $67.07 | $63.66 | $-3.41 | $0.29 | $-3.12 | -0.0465 |
| 2021 | 7 | $63.66 | $62.83 | $-0.83 | $0.00 | $-0.83 | -0.0130 |
| 2021 | 8 | $62.83 | $64.15 | $1.32 | $0.00 | $1.32 | 0.0210 |
| 2021 | 9 | $64.15 | $61.66 | $-2.49 | $0.37 | $-2.12 | -0.0331 |
| 2021 | 10 | $61.66 | $64.13 | $2.47 | $0.00 | $2.47 | 0.0401 |
| 2021 | 11 | $64.13 | $62.89 | $-1.24 | $0.00 | $-1.24 | -0.0193 |
| 2021 | 12 | $62.89 | $66.88 | $3.99 | $0.47 | $4.46 | 0.0708 |
| 2022 | 1 | $66.88 | $63.87 | $-3.01 | $0.00 | $-3.01 | -0.0450 |
| 2022 | 2 | $63.87 | $64.61 | $0.74 | $0.00 | $0.74 | 0.0116 |
| 2022 | 3 | $64.61 | $64.60 | $-0.01 | $0.29 | $0.28 | 0.0044 |
| 2022 | 4 | $64.60 | $60.84 | $-3.76 | $0.00 | $-3.76 | -0.0582 |
| 2022 | 5 | $60.84 | $62.35 | $1.51 | $0.00 | $1.51 | 0.0248 |
| 2022 | 6 | $62.35 | $58.76 | $-3.59 | $0.31 | $-3.28 | -0.0527 |
| 2022 | 7 | $58.76 | $62.59 | $3.83 | $0.00 | $3.83 | 0.0652 |
| 2022 | 8 | $62.59 | $60.88 | $-1.71 | $0.00 | $-1.71 | -0.0273 |
| 2022 | 9 | $60.88 | $55.50 | $-5.38 | $0.39 | $-4.99 | -0.0820 |
| 2022 | 10 | $55.50 | $60.99 | $5.49 | $0.00 | $5.49 | 0.0989 |
| 2022 | 11 | $60.99 | $65.47 | $4.48 | $0.00 | $4.48 | 0.0735 |
| 2022 | 12 | $65.47 | $61.37 | $-4.10 | $0.55 | $-3.55 | -0.0542 |
| 2023 | 1 | $61.37 | $64.48 | $3.11 | $0.00 | $3.11 | 0.0506 |
| 2023 | 2 | $64.48 | $65.10 | $0.62 | $0.00 | $0.62 | 0.0097 |
| 2023 | 3 | $65.10 | $59.74 | $-5.36 | $0.00 | $-5.36 | -0.0823 |
| 98 records | -0.3219 |
Step 2: Calculate the average monthly gain/loss percent
-0.3219/98=-0.003284693877551
Step 3: Calculate the standard deviation of the monthly gain/loss percent
0.11033396552918819
We just used a SQL query on the database: 'Select stddev(gainlosspercent) from Returnsmonthly where symbol='SMDV' group by symbol'
Step 4: Take the average monthly gain/loss percent and divide by the standard deviation of the monthly gain/loss percent
-0.003284693877551/0.11033396552918819=-0.029770468792605
Step 5: Multiply that number times 3.46410161514 (the square root of 12)
-0.029770468792605*3.46410161514=-0.10312792902794
This is the tricky step that is only necessary because we are using monthly returns. We got this from Morningstar's documentation.
Conclusion: SMDV's Sharpe Ratio is -0.10
SPY's Sharpe Ratio during the same time period was 0.7193. Let's look at a price chart of SMDV compared to SPY:
SMDV has under performed SPY on a risk adjusted basis using the Sharpe Ratio. SMDV's returns have been more volatile compared to SPY's returns, measured using standard deviation. SMDV's standard deviation of returns has been 38.42% whereas the standard deviation of SPY's returns during the same time period has been 15.85%.
All data is a live query from our database. The wording was last updated: 05/02/2020.
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