Econometrics Lecture: “Alpha and Beta”
David M. Gross, Ph.D.
Motivating Questions:
1. How much market risk do you have?
How do you measure market risk?
2. You beat the market? What’s your alpha? What’s your beta?
Never pay for beta. Only pay for alpha.
3. What’s your oil sensitivity? How much oil risk do you want?
Outline:
1. Measuring Market risk
2. Measuring Manager Performance
3. Measuring Risk-Factor Sensitivity
The basic model:
y =  + X + u
1. Measuring Market risk
Market Risk
A stocks price reflects current and expected value
Depends on economy, industry, company
How do we measure changes in the economy? GDP: quarterly calculations
Proxy for changes in expectations about the economy: S&P 500
r – rf =  +  rM - rf  + u







r = the return on a stock/portfolio
rf = the risk free return
rM = the market return (market proxies: e.g. the S&P 500)
historic rM = about 8.4%
(r – rf ) = the risk premium of the stock/portfolio
 rM - rf = the market’s risk premium
 = the risk-adjusted excess return of the stock/portfolio
 > 1 luxury, high end retail
 = 1 mid retail, durables, office equipment
 < 1 necessities, soap, food…
<<Show Beta Table 1>>
Table 1
Company Betas from Google Finance:
Symbol
Beta
Procter and Gamble
PG
0.37
1
Altria
Wal-Mart
Office Max
Target
Apple
AT&T
Level 3
Qwest
MO
WMT
OMX
TGT
AAPL
T
LVLT
Q
0.42
0.50
1.05
1.20
1.32
1.54
2.27
2.50
Non-Market Risk
1 – R2 = SSR/SST
Idiosyncratic risk, unique,
Easily eliminated through diversification
Those who diversify will require a lower return, pay more, so no compensation for diversifiable
risk  CAPM (Capital Asset Pricing Model)
E(r) – rf = [E(rM) – rf]
E(r) = rf + [E(rM) – rf]
What if hold high beta stocks and the market is up?
The CAPM says I should have a return that exceeds the market’s return.
2. Manager Performance
You beat the market?
Adjust for risk:
Example:
r =15%;  = 2; rM = 10%; rf = 3%
“Beat the market” since 15% > 10%
Ex-post (CAPM is ex-ante):
r – rf = (rM – rf)
r = rf + (rM – rf)
r = 0.03 + 2(0.10 – 0.03) = 0.03 + 2(0.07) = 0.03 + 0.14 = 0.17
15% < 17%
So didn’t beat the market on a risk-adjusted basis
r – rf =  +  rM - rf  + u
 = r – rf – (rM – rf) = 0.15 – 0.03 – 2(0.10 – 0.03) = 0.15 – 0.03 – 0.014 = -0.02
 = -0.02
 = the risk-adjusted excess return
<<Show Alpha and Beta Table 2>>
Table 2
2
Estimated Betas and Alphas from 5 years of monthly data through 8/2007
Portfolio
Return
Beta
Alpha
S&P 500
9.98%
1.00
0.00
(0.00)
(0.00)
EVTMX
22.62%
0.73
0.15
(0.00)
(0.00)
FELBX
12.16%
2.16
-0.06
(0.00)
(0.44)
Hedge Fund 1
18.60%
0.79
0.10
(0.00)
(0.02)
Hedge Fund 2
20.02%
1.94
-0.07
(0.00)
(0.05)
3. Risk Factors
Define risk factors (energy, $, interest rates, …)
4. Use regressions to measure Factor Sensitivity
5. Use wine importer example to motivate $/Euro risk
Model:
(r – rf) =  +  rM – rf + F1 rF1 – rM + F2 rF2 – rM + … + u
<<Show Oil Beta Table 3>>
Table 3
Estimated Betas from 5 years of monthly data through 8/2007
Which firm is the airline? Which is the oil company?
Beta Market
Beta Oil
Firm A
0.99
0.35
(0.00)
(0.00)
Firm B
1.78
-0.54
(0.00)
(0.03)
Which one is the airline? Which is the oil company?
Multi-factor alpha:
 = the multi-factor risk-adjusted excess return
Used by Morningstar (Describe Morningstar)
3