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Asset Pricing Theory in One Lecture Eric Falkenstein 1 Finding Alpha.
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Transcript of Asset Pricing Theory in One Lecture Eric Falkenstein 1 Finding Alpha.
Capital Asset Pricing Model (CAPM)Arbitrage Pricing Model (APT)Stochastic Discount Factor Model (SDF)General Equilibrium Theory
2Finding Alpha
1. Monopoly power2. Uncertainty (Frank Knight)3. Entrepreneur (Schumpeter)4. Return on Capital Profits should go to zero over time (Das
Kapital) Modern Portfolio Theory: Return for bearing
‘risk’
3Finding Alpha
Diversification, Diminishing Marginal Utility
Processes:Arbitrage Equilibrium
4Finding Alpha
E[Reti]=+Eif
DiversificationDecreasing marginal utility
Util
ity
Consumption
Portf
olio
Vol
# assets
St. Petersburg Paradox (1738): what is value of $1 paid if you get a head in a coin flip, where the payoff is (number of times coin flipped)^2?
Should be infinity
Why not? Diminishing marginal returns
5Finding Alpha
1
1 1 1 11 2 4 8 ...
2 4 4 161 1 1 1
...2 2 2 2
1
2j
E
E
E
Jevons, Menger, Walras noted diminishing marginal utility could explain pricing
6Finding Alpha
0, 0U W U W
7Finding Alpha
Johnny Von Neumann and Oscar Mortgenstern 1941 Theory of GamesMilton Friedman and Savage 1947
Why not put all your wealth in one stock?
“To suppose that safety-first consists in having a small gamble in a large number of
different [companies] … strikes me as a travesty of investment policy.”
Keynes
8Finding Alpha
Finding Alpha 15
Standard Deviation
Expected Return
100% investment in security with highest E(R)
100% investment in minimum variance portfolio
No points plot above the red line
All portfolios on the red line are efficient
Why we like efficient portfolios
Portfolio Selection: Efficient Diversification of Investments (1959)
Markowitz preferred ‘semi-variance’ in bookAlso examines:
standard deviation, expected value of loss, expected absolute deviation, probability of loss, maximum loss
‘Prospect Theory’ in 1952
16Finding Alpha
Levy and Markowitz (1979) show the mean-variance optimization is an excellent approximation to expected utility when not-normal
”[in the 1960s] there was lots of interest in this issue for about ten years. Then academics lost interest. “
Eugene Fama
23Finding Alpha
1. every asset has same marg. valuei imaE r k
2. f fm fE r a k kr
22
3. m f
mm mE r a k a
E r r
2
4. i im
fm f
m
E r rrE r
25. im
f m fm
iE r r E r r
6. aka the CAPM the SMLi f m fiE r r E r r
Finding Alpha 24
Beta
Expected Return
Rf
Market Portfolio
1.0
E(R)
( ) ( )
where ( ) expected return on security
risk-free rate of interest
beta of Security
( ) expected return on the market
i f i m f
i
f
i
m
E R R E R R
E R i
R
i
E R
Finding Alpha 25
'
' ' 10 1 '
0
U1. U U 1 1 1
UE r E r
3. [ ] [ ] [ ] cov( , ) 1E MR E M E R M R
1
[ ]
c4.
ov( , ]
[ ][
)E
M
M
E
R
E MR
15. [ ]
[ ]ff RE RE M
'1' '0 0
'0
-U6.
U U
1 cov( , )
' cov( , )
m
m
i mR
RM
U M RR
UR
'0' '
01
cov( ,7.
)[ ] i m
fEU
RR R
U UR
'1'0
2. 1 givU
Uen M=E MR
'1
cov( , )8. [ ] i m
f
R RE R R
U
cov( , )11. [ ] [ ]
var( )i m
i f m fm
R RE R R E R R
R
12. [ ] [ ]i f m fE R R E R R
'1
var( )9. letting R =R
[ ]m
i mm f
RU
E R R
cov( , )10. [ ]
var( )
[ ]
i mf
m
m f
R RE R R
R
E R R
26Finding Alpha
1 E MR
1 1,2, ,
k
i i ji j ij
r a b f e i n
1 1 1' , , m
M U R GDP oil
Total Ut
Marginal Ut
Wealth
T-bills, MT Tbonds, LT Treasuries, Corp Bonds, Mortgages, Large Cap Stocks, Large-cap growth stocks, medium cap stocks, small cap stocks, non-US bonds, European stocks, Japanese stocks
If f is a risk factor, it must have a linear price to prevent arbitrage
Can of beer: $16-pack of beer: $6Case of beer (24 pack): $24Price of beer linear in units, else arbitrage
27Finding Alpha
1 1 2 2
Random'price of risk''how much'
,
0
1,2, ,
~
f i
j j j
j
i iibr r f b f e i n
f N
Finding Alpha 28
For k number factors
How many factors? 3? 5? 12?What are the factors? Empirical issue.Could be estimated just like a ‘bias’Total Portfolio Volatility no longer the issue
1 1,2, ,
k
i i ji j ij
r a b f e i n
f m m f size small big value value growth mo up downi r r r r r r r r rr
Markowitz. Normative model: people should invest in efficient portfoliosNo residual aka idiosyncratic aka unsystematic,
volatilityTobin: Efficient portfolio always combination
of a single risky portfolio and the non-risky asset
Sharpe : Given Tobin, covariance with the market dictate expected return
Ross: add factors like Rm-Rf , whatever matters to people, linear pricing in factors
29Finding Alpha