Percentage Returns:
Div Yield
+ Capital Gain
Total Return
=
Div(t+1) / P(t)
+ (P(t+1) – Pt) / P(t)
R(t+1)
=
.05
+ .09
=
.15
Suppose you had 5k invested
Total dollar return = 5k x .15
If you know the total dollar return on the stock
You do not
need to know how many shares you would have to
purchase to figure out how much money you would have made.
Three year holding period return
(1 + R1) x (1 + R2) x (1 + R3) = 1.15 (15% total return … holding
period return)
Ch. 10:
Variance / Standard Deviation Calculation:
1. Calculate expected return:
Average Return (A)
=
Abar
=
.175
Average Return (B)
=
Bbar
=
.055
2. Deviation from expected return:
RA – Abar
(For each state)
3. Square each deviation
4. Average of all the squares = Variance
5. Sq. Rt. Of Variance = St. Deviation
OR:
Var(Rn) = Expected valued of (Rn – Rbar)^2
Covariance and Correlation:
1. Multiply respective deviations / residuals together
2. Come up with an average of multiplied residuals
Cov (Ra,Rb) = Expcected (Avg.) of Residuals
1. A’s return generally above its avg. when B’s return above avg
positive dependency / relationship … POSITIVE Covariance
2. A’s
return generally about avg. when B’s below B’s avg.
Negative Covariance
3. No relation = Covariance of 0
Correlation (A,B) = Covariance (A,B) / (St. DevA x S. DevB)
Var (Port) = (XaVar (a))^2 + 2XaXbCov(a,b) + (XbVar(b))^2
NOTE: Cov(a,b) = Corr(a,b) x SD(A) x SD(B)
1. Expected Return of the Portfolio = Xa E(a) + Xb E(b)
= .60(.175) + .40 (.055)
= .127
Note: a positive relationship or Cov between variables increases the
variance for the entire portfolio which is undesirable
As long as Corr < 1 … SD(port) is < Wt avg of a and b
DIVERSIFICATION
The Efficient Set for Two Assets:
1. Diversification occurs when Corr < 1
2. MV = minimum Var / minimum SD
3. Cannot achieve point outside feasible set b/c cannot decrease SD
of securites or correlation between securites
How can an increase in the proportion of risky security (B)?
Due to diversification effect.
Risk of portfolio is reduced thus
backward bending
. Eventually the
high SD of B
causes the SD of
the entire portfolio to rise
5. No investor
would want to hold a portfolio with an expected
return below that of the MV portfolio
6. Straight Line comes form Corr = 1 (No diversification)
Variance(port) (As N tends to Infinity) = CovBar
*** Variance(port) (As N tends to Infinity) = CovBar ***
Optimal Portfolio:
LINE 2: Efficient set of all assets
(1) m = intercept = Rf = Riskfree rate
(2) Line tangential to optimal curve
(3) All $ in Pt. A, just how much to Lend/Borrow
Market Equilibrium Portfolio:
*In a world with homogenous expectations, all investors would
hold the portfolio of risky assets represented by point A
1 Estimate expected returns and var for individuals securities
2 Covariances btwn pairs of securiteies
3 Efficient set of risky assets
4 Pt A from line 2
5 choose pt based on internal characteristics such as risk advers
Plot expected returns for Market and Stock in each State
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 Spring '10
 jaffe
 Corporate Finance

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