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10‐30 Class 10: Market efficiency
Investors and Alpha and BetaProblems with CAPM
Variation in the price of risk Variation in alpha.Variation in alpha.Your portfolios
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Lessons from CAPMLessons from CAPM
• Future stock returns are predicted byp y
• (1) the riskless return
• (2) the amount of systematic risk in a security(2) the amount of systematic risk in a security times the price of risk
• So if model is right you can “make” money (earn• So if model is right you can make money (earn above the risk free rate) only if you bear risk
• If model is wrong by taking advantage of its• If model is wrong by taking advantage of its anomalies.
2
Staying with the modelStaying with the model
• Chasing βChasing β– The return to bearing risk is positive– And possibly largep y g– But there are down sides
• Works if you can be patientWorks if you can be patient• Attractive when the price of the riskless asset is lowis low
• So Fed pushes down interest rates => bearing risk more attractive s o e att act e
3
Annualized Monthly Returns of the S&P‐500 (R ) f 3 TBill (R )(RM)net of 3 year TBill return (RF)
200.00%
150.00%
RF
RM‐RF
Poly. (RM‐RF)
50.00%
100.00%15 per. Mov. Avg. (RM‐RF)
0.00%10/19/1989 7/15/1992 4/11/1995 1/5/1998 10/1/2000 6/28/2003 3/24/2006 12/18/2008 9/14/2011
100 00%
‐50.00%
‐100.00%
4
From Previous slideFrom Previous slide
• Clearly see moments 200.00%Clearly see moments when the price of risk is low
150.00%
• And when it is high.
• Look at moving average 50.00%
100.00%
g g
• Also note the choice of the riskless rate is
0.00%9/9/2008 9/9/2009 9/9/2010 9/9/2011
pretty irrelevant
100 00%
‐50.00% RFRM‐RFPoly. (RM‐RF)15 per Mov Avg (RM‐RF)‐100.00% 15 per. Mov. Avg. (RM‐RF)
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High β vs low βHigh β vs low β
• Two interpretationsTwo interpretations• From Investor
– If β is high firm is very exposed to systematic riskIf β is high, firm is very exposed to systematic risk– You have to pay the investor to bear that risk– If β is low, investor wants a smaller share of theIf β is low, investor wants a smaller share of the total return per dollar he or she spends
• From Firm– High β cost of equity is high – Low β cost of equity is low
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Distribution of β in your firmsDistribution of β in your firms6
Week 3 and 4 firms
3
4
5Week 3 and 4 firms
Week 2 firms
Linear (Week 3 and 4 firms)
1
2
3
BETA
2
‐1
00 2 4 6 8 10 12 14 16 18
‐4
‐3
‐2
Coeficient of Variation of Prices 10‐9 to 10‐25
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Are β correlated with firm returnsAre β correlated with firm returns 60.0
20 0
40.0W3 return
W4 return
Linear (W3 return)
( )
0.0
20.0
‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5 6
Linear (W4 return)
‐20.0
‐40.0
‐60.0
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Short run result!Short run result!20.0
10.0
15.0
W3 returnW4 returnLinear (W3 return)
0.0
5.0
Linear (W3 return)Linear (W4 return)
10 0
‐5.0
‐2 ‐1 0 1 2 3 4
‐15.0
‐10.0
‐20.0
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In the short runIn the short run
• It’s the noise (ε) that dominatesIt s the noise (ε) that dominates
• You cannot estimate β off of two weeks
h h i i l h• But these have statistical power over the longer term
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Beta correlated with short term variation?
4
5
6
2
3
4
‐1
0
1
0 2 4 6 8 10 12 14 16 18
‐3
‐2
‐1
Beta
Linear (Beta)
‐4
Horizontal axis is the coefficient of variation (st. deviation/average) of i i l i i β d b h fi S fi h
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price. Vertical axis is β reported by Yahoo finance. Some firms have no reported β.
Beta correlated with short term variation?
4
5
1
2
3
‐1
0
1
0 1 2 3 4 5 6
‐3
‐2 Beta
Linear (Beta)
‐4
Notice large number of firms with very similar β and very different σ.
12
If not β then α?If not β then α?
• Recall from last class that we estimate the following grelationship
• Β is fine, but you have to bear risk.• Why not pick high α firms?Th fi h t b th i k f t• These are firm where returns above the risk free rate are larger than CAPM would predict
• Expect these firms to get bid up (α should disappear)Expect these firms to get bid up (α should disappear)• Problem is that α estimate are very sensitive to sample and period.
13
Beyond our dataBeyond our data
• Problems with CAPMProblems with CAPM
h d l k if d l if h• The model work if and only if no other variable enters the regression (because of the
d f h ld h kneed for everyone to hold the market portfolio)
• In other words the model works if the market is efficient (prices are all you need)
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Fama and French 2006Fama and French 2006
• Value (high book to market value B/M) Vs growth a ue ( g boo to a et a ue / ) s g o t(low book to market value) stocks
• “When we form portfolios on size, B/M, and β, p βwe find that variation in β related to size and B/M is compensated in average returns for 1928 to 1963 b t i ti i β l t d t i d B/M1963, but variation in β unrelated to size and B/M goes unrewarded the sample period (1929‐2004). […] We conclude that it is size and B/M, or risks[…] We conclude that it is size and B/M, or risks related to them, and not β, that are rewarded in average returns.”
15
Fama and French 2006 (cont)Fama and French 2006 (cont)
• What does matter beyond β?
• Small firms have 0 2% return per0.2% return per month over large firms
• Value (high book to market) have a 0 35% return
Figure 1. Each week from 1983 to 2003, we rank stocks based on their returns over the prior week and0.35% return
premium over growth firms
stocks based on their returns over the prior week and form a portfolio comprised of a long position in the top decile of stocks (winners) and a short position in the bottom decile (losers). Gutierrez and Kelley JOURNAL OF FINANCE VOL FEB 2008
• MomentumJOURNAL OF FINANCE VOL. FEB. 2008
Replace CAPM with an empirical d lmodel
• Add as many factors as you likey y• In their case
– β (more is good)– Book to market value (higher is better)– Size (large is bad)– Momentum (past increase lingers)Momentum (past increase lingers)
• Then as you use these factors in choosing weights you bid up the stocks with higher returns and
h ld ‘ ” d lreturn the world to a ‘pure” CAPM model• Except you may never get there.
17
Some evidence of efficiency
40.0
60.0
20.0
0.0‐4 ‐3 ‐2 ‐1 0 1 2 3 4 5 6
Poly. ()
‐40.0
‐20.0
‐60.0
18
Return to your stocks from Week 1 to Week 2
Returns of your portfolios ( b )(above S&P 500)
30.00%
20.00%
25.00%
10.00%
15.00%
0.00%
5.00%
‐5.00% ‐4.00% ‐3.00% ‐2.00% ‐1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
‐10.00%
‐5.00%
Here we seem to have a classic momentum effect driven by a small number of
19
Here we seem to have a classic momentum effect driven by a small number of portfolios. (most did just about the same week 1 as the S&P)
Are portfolio’s useful?Are portfolio s useful?20.00%
10.00%
15.00%
Stock Returns 10‐9 to 10‐25
0.00%
5.00%
0 00% 2 00% 4 00% 6 00% 8 00% 10 00% 12 00%
Portfolios Returns 10‐9 to 10‐25
‐10.00%
‐5.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
‐15.00%
10.00%
20
Not if you want to win the investment derby when you can only go long on stocks.
‐20.00%
• Notice portfolios are 10.00%
Stock Returns 10‐9 to 10‐25
f lp
left leaning• Offer similar returns but l
5.00%
Portfolios Returns 10‐9 to 10‐25
lower variance• Could go and find set of stock with similar 0.00%stock with similar expected returns as week 1
5 00%
0.00%0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
• But also a lot of dominated portfolios
‐5.00%
21
‐10.00%
Did you beat the market?Did you beat the market?
• Make a random pickp• Your chance of beating the market are 50‐50
– 29% of week 2 stocks beat the market week 3– 41% portfolios the market week 3 41% – 50% of week 2 stocks beat the market week 4– 61% portfolios beat the market week 461% portfolios beat the market week 4
• Make two consecutive picks 25%(LL) 50%(LW or WL) and 25% (WW)– 28% LL stocks 65% LW‐WL and 7%WW– 22% LL portfolios, 52%WL‐LW and 26% WW
22
11‐04 Class 11: Intermediaries and assets
• Intermediaries DefinitionIntermediaries Definition
• There are still spreads
i f i• creating new assets: Transformation; Bundling;
• Unbundling;
• Taking positions g p
• Leverage
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