What Is The Sharpe Ratio?

Introduction

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 Vary

Sharpe Ratio calculations tend to vary, for several reasons:

We believe the important point is that it does not matter which exact formula you use, as long as you consistently apply the same formula to all stocks, ETFs and portfolios you are comparing. Just be consistent. The point is to compare SMDV to SPY, not that SMDV should have a certain "target" Sharpe Ratio.

Our Calculations

We calculate our own Sharpe Ratios for all ETFs. Our calculations are done in the following manner:

Keep in mind that for older ETFs, our calculations may generate a Sharpe Ratio that seems low. If you are used to looking at Sharpe Ratios calculated using 3 or 5 year return periods, those numbers are going to be pretty high, because we have been in the middle of a historic bull run. We are calculating Sharpe Ratios using returns from the lifetime of an ETF.

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 0.4320. 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 0.4803.

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.

Benchmark Sharpe Ratios

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.

Example Calculation Using SMDV

Step 1 - Build a table showing average returns by month, during the entire lifetime of the ETF (from inception until today):

YearMonthOpening PriceClosing PriceGain (loss)DividendTotal Gain (loss)Gain (loss) %
20152$39.98$40.21$0.23$0.00$0.230.0058
20153$40.21$40.38$0.17$0.14$0.310.0076
20154$40.38$39.37$-1.01$0.00$-1.01-0.0250
20155$39.37$39.57$0.20$0.00$0.200.0051
20156$39.57$40.30$0.73$0.16$0.890.0224
20157$40.30$40.47$0.17$0.00$0.170.0042
20158$40.47$38.48$-1.99$0.00$-1.99-0.0491
20159$38.48$37.95$-0.53$0.18$-0.35-0.0090
201510$37.95$40.99$3.04$0.00$3.040.0801
201511$40.99$41.87$0.88$0.00$0.880.0215
201512$41.87$40.21$-1.66$0.25$-1.41-0.0336
20161$40.21$39.72$-0.49$0.00$-0.49-0.0122
20162$39.72$41.23$1.51$0.00$1.510.0380
20163$41.23$43.53$2.30$0.16$2.460.0596
20164$43.53$43.49$-0.04$0.00$-0.04-0.0009
20165$43.49$44.82$1.33$0.00$1.330.0306
20166$44.82$46.98$2.16$0.15$2.310.0515
20167$46.98$47.74$0.76$0.00$0.760.0162
20168$47.74$47.56$-0.18$0.00$-0.18-0.0038
20169$47.56$47.77$0.21$0.16$0.370.0078
201610$47.77$47.02$-0.75$0.00$-0.75-0.0157
201611$47.02$51.42$4.40$0.00$4.400.0936
201612$51.42$53.74$2.32$0.26$2.580.0502
20171$53.74$52.67$-1.07$0.00$-1.07-0.0199
20172$52.67$53.45$0.78$0.00$0.780.0148
20173$53.45$53.12$-0.33$0.16$-0.17-0.0031
20174$53.12$54.22$1.10$0.00$1.100.0207
20175$54.22$53.32$-0.90$0.00$-0.90-0.0166
20176$53.32$54.48$1.16$0.23$1.390.0261
20177$54.48$55.31$0.83$0.00$0.830.0152
20178$55.31$54.07$-1.24$0.00$-1.24-0.0224
20179$54.07$56.07$2.00$0.28$2.280.0421
201710$56.07$56.08$0.01$0.00$0.010.0002
201711$56.08$57.89$1.81$0.00$1.810.0323
201712$57.89$55.19$-2.70$0.34$-2.36-0.0407
20181$55.19$55.23$0.04$0.00$0.040.0007
20182$55.23$52.55$-2.68$0.00$-2.68-0.0485
20183$52.55$53.63$1.08$0.16$1.240.0235
20184$53.63$54.30$0.67$0.00$0.670.0125
20185$54.30$56.29$1.99$0.00$1.990.0366
20186$56.29$57.15$0.86$0.30$1.160.0206
20187$57.15$58.44$1.29$0.00$1.290.0226
20188$58.44$59.38$0.94$0.00$0.940.0161
20189$59.38$58.88$-0.50$0.23$-0.27-0.0045
201810$58.88$55.64$-3.25$0.00$-3.25-0.0551
201811$55.64$58.87$3.24$0.00$3.240.0581
201812$58.87$53.83$-5.05$0.38$-4.67-0.0793
20191$53.83$57.50$3.68$0.00$3.680.0683
20192$57.50$59.52$2.02$0.00$2.020.0351
20193$59.52$58.25$-1.27$0.19$-1.08-0.0181
20194$58.25$59.69$1.44$0.00$1.440.0247
20195$59.69$57.17$-2.52$0.00$-2.52-0.0422
20196$57.17$59.65$2.48$0.36$2.840.0496
20197$59.65$59.36$-0.29$0.00$-0.29-0.0049
20198$59.36$57.47$-1.89$0.00$-1.89-0.0318
20199$57.47$59.36$1.89$0.30$2.190.0381
201910$59.36$61.02$1.66$0.00$1.660.0280
201911$61.02$60.73$-0.29$0.00$-0.29-0.0048
201912$60.73$61.79$1.06$0.41$1.470.0242
20201$61.79$60.17$-1.62$0.00$-1.62-0.0262
20202$60.17$53.96$-6.21$0.00$-6.21-0.1032
20203$53.96$46.23$-7.73$0.28$-7.45-0.1381
20204$46.23$48.47$2.24$0.00$2.240.0485
20205$48.47$49.68$1.21$0.00$1.210.0250
20206$49.68$48.48$-1.20$0.29$-0.91-0.0183
20207$48.48$48.18$-0.30$0.00$-0.30-0.0063
20208$48.18$0.00$-48.18$0.00$-48.18-1.0000
20209$0.00$48.73$48.73$0.00$48.730.0000
68 records-0.6555

Step 2: Calculate the average monthly gain/loss percent


-0.6555/68=-0.0096397058823529


Step 3: Calculate the standard deviation of the monthly gain/loss percent


0.1272033655905399

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


-0.0096397058823529/0.1272033655905399=-0.075781846161072


Step 5: Multiply that number times 3.46410161514 (the square root of 12)


-0.075781846161072*3.46410161514=-0.26251601568486

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 -0.26

SPY's Sharpe Ratio during the same time period was 0.8516. 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 44.39% whereas the standard deviation of SPY's returns during the same time period has been 14.53%.


All data is a live query from our database. The wording was last updated: 05/02/2020.

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