Unformatted text preview: . Theoretically, alpha
measures
”.
should be zero; however, empirical evidence suggests
that alpha exists for various reasons (unidentified risk
exposures, mispricing, market friction, etc.)
exposures,
543
– ε denotes the regression errors, let it be zero now
denotes From Sharpe ratio to CAPM (1)
Since we have learned the intuition of Sharpe ratio,
Since
can we use the intuition to learn CAPM?
can
The answer is: Yes
Deriving CAPM from Sharpe ratio:
For stock i, it’s Sharpe = [E(ri)  rf ] / σi
For market portfolio, it’s Sharpe = [E(rm)  rf ] / σm
For
Then, in equilibrium and no arbitrage (assuming
that vol. is the only risk), these two Sharpe ratios
should be equal, i.e., [E(ri)  rf ] = (σi / σm) [E(rm)  rf ],
[E(r
which is a CAPM model
which
544 From Sharpe ratio to CAPM (2)
Deriving Sharpe ratio from CAPM:
The Sharpe ratio equilibrium exists when
ri  rf = β [ rm  rf ]
then Var(ri  rf) = E[(ri  rf)2] –{E[(ri  rf)]} 2
then
= β2 Var(rm  rf)
Var(r
and β = σi / σm
[E(ri)  rf ] = (σi / σm) [E(rm)  rf ]
[E(r
[E(ri)  rf ]/ σi = [E(rm)  rf ]/ σm
[E(r
Sharpe of firm i = Sharpe of market
Sharpe
545 Simple examples
Assume E(rm) = 0.11, rf = 0.03, and α = 0
For stock x with βx = 1.25, then
For
1.25,
E(rx) = 0.03 + 0 + 1.25(0.08) = .130 or 13.0%
For stock y with βy = 0.6, then
For
E(ry) = 0.03 + 0 +0.6(0.08) = .078 or 7.8% 546 Tradeoff between market risk exposure
(β) and expected return
E(r) rx=13%
r0=11%
ry=7.8%
3%
0.6 1.0 1.25
ßy ß0 ßx ß
547 Estimating the CAPM using Real Data
Using historical data on Tbill, S&P 500 and
Using
individual securities
individual
Regressing individual stock’s excess returns on
Regressing
the S&P 500’s excess returns
the
(Riskfree rate source:
Riskfree
http://www.treasury.gov/offices/domesticfinance/debthttp://www.treasury.gov/offices/domesticfinance/debtmanagement/interestrate/daily_treas_bill_rates.shtml) Now, data are: “DELL” and “SP500” and “CAPM”
Now,
in Lecture2_StockPricing
in
548...
View
Full Document
 Spring '09
 returns

Click to edit the document details