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?

  1. You beat the market? What’s your alpha? What’s your beta?

Never pay for beta. Only pay for alpha.

  1. 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

 = 1mid retail, durables, office equipment

 < 1necessities, soap, food…

<Show Beta Table 1

Table 1

Company Betas from Google Finance:

Symbol / Beta
Procter and Gamble / PG / 0.37
Altria / MO / 0.42
Wal-Mart / WMT / 0.50
Office Max / OMX / 1.05
Target / TGT / 1.20
Apple / AAPL / 1.32
AT&T / T / 1.54
Level 3 / LVLT / 2.27
Qwest / Q / 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.

  1. 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

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)
  1. Risk Factors

Define risk factors (energy, $, interest rates, …)

  1. Use regressions to measure Factor Sensitivity
  2. 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)

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