8/23/16
MEASURING RISK AND RETURN:
AN ILLUSTRATION
WHAT WILL YOU LEARN?
Welook at past returns on four stocks and compute the
average annual return and volatility from historical
monthly data.
Youwill learn how to summarize the past returns on an
asset.
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WHICH ASSET IS BETTER?
Prob.
A B
return
WHICH ASSET IS BETTER?
Prob. Prob.
X
A B
Y
return return
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WHICH ASSET IS BETTER?
Prob.
return
MONTHLY HISTORICAL DATA
APPLE WALMART IBM NIKE
1/31/11 5.20% 3.97% 10.38% -3.44%
… ... ... ... ...
1/31/14 -10.77% -5.10% -5.81% -7.36%
2/28/14 5.75% 0.03% 5.38% 7.81%
3/31/14 2.00% 2.98% 3.95% -5.67%
4/30/14 9.94% 4.29% 2.07% -1.23%
5/30/14 7.87% -3.09% -5.62% 5.76%
6/30/14 2.77% -2.21% -1.68% 0.83%
7/31/14 2.87% -1.98% 5.74% -0.54%
8/29/14 7.75% 3.29% 0.92% 2.15%
9/30/14 -1.71% 1.28% -1.28% 13.56%
10/31/14 7.20% -0.26% -13.40% 4.23%
11/28/14 10.60% 14.78% -0.68% 6.80%
12/31/14 -7.19% -1.35% -1.07% -2.88%
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AVERAGE RETURN AND VOLATILITY
APPL WALMART IBM NIKE
Average monthly return 1.755% 0.540% 0.177% 2.103%
Monthly volatility 7.145% 4.815% 4.545% 6.098%
AVERAGE RETURN AND VOLATILITY
APPL WALMART IBM NIKE
Average monthly return 1.755% 0.540% 0.177% 2.103%
Monthly volatility 7.145% 4.815% 4.545% 6.098%
APPL WALMART IBM NIKE
Average annual return 21.062% 6.483% 2.123% 25.234%
Annual volatility 24.750% 16.680% 15.744% 21.125%
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Average annual return and volatility
2011-2015
30.0%
NIKE
AVERAGE ANNUAL RETURN
25.0%
APPLE
20.0%
15.0%
10.0%
WALMART
5.0%
IBM
0.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0%
ANNUAL VOLATILITY
SUMMARY
You learned to compute the average return and volatility from a time series
of returns.
You learned to annualize average return and volatility.
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HISTORICAL RECORD ON RISK &
RETURN PATTERNS
WHAT WILL YOU LEARN?
Historical data on risk and return patterns
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SUMMARY STATISTICS OF ANNUAL TOTAL
RETURNS FROM 1926 TO 2009
Average Standard
Annual Ret. Deviation Distribution
Large stocks 9.8% 20.5%
Small stocks 11.9 52.8
Long-term corp. bonds 5.9 8.3
Long-term govt. bonds 5.4 8.7
U.S. Treasury bills 3.7 3.1
Inflation 3.0 4.2
– 90% 0% + 90%
The Empirical Distribution of Annual Returns for U.S. Large stocks (S&P 500), Small Stocks,
Treasury Bonds and Treasury Bills (1926-2012)
Treasury Bills
60
Frequency
40
20
0
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Long-term Treasury Bonds
30
Frequency
20
10
0
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Large Stocks
10
Frequency
0
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Small stocks
10
Frequency
0
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
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Historical risk-return trade-off
20.000
18.000
Small stocks
16.000
14.000
Historical average return
12.000
S&P 500
10.000
World stocks
8.000
6.000 World Bonds
Treasury Bonds
4.000 Treasury Bills
Inflation
2.000
0.000
0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000
Standard Deviation
FROM HISTORICAL DATA TO EXPECTED
RETURNS
Where do we come up with expected returns?
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8/23/16
HISTORICAL AVERAGE RETURNS
Theidea is if expected returns are constant over time, long-
run average realized returns is a good estimate of expected
future returns.
Should you think twice before using historical returns as
forecasts of future returns?
YES! Why?
HISTORICAL AVERAGE RETURNS
Any sample period may be biased.
Longerhistorical window reduce sample specificity and give
more accurate estimates
Wouldyou want to include data from 1600s even if good quality
data were available to us?
Expected returns may vary in cyclical fashion.
Forspecific funds and strategies, historical performance is
often upward biased: Voluntary reporting or survivorship
bias. Same point with simulated ‘paper’ portfolios that ignore
trading costs.
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8/23/16
SUMMARY
Investors face a risk-return trade-off.
Riskier investments have on average had higher
returns.
Bevery careful on using historical data to come up
with forecasts of expected returns.
