Calculating Portfolio Riskσ^{2}=Wa ^{2}σa ^{2}+Wb ^{2}σb ^{2}+2(Wa Wb Cor σa σb )  σx =standard deviation  σ^{2}= variance of portfolio  Wx = weight of stock in portfolio  Covariance of stocks = correlation *σa *σb  σ = risk of an individual stock  ß = Market risk 
If you need to find out the standard deviation, take the square root of the answer. Variance, leave it squared.
Book Rate of ReturnBook Rate of Return=  Book income/book assets 
Payback & Discounted Payback PeriodPayback = # of years to payback investment (no NPV adjustment)  Discounted = # of years to payback investment NPV adjustment)  NPV= C0 +(C1 /(1+r1 ))+(C2 /(1+r2 ))..............(Ct /(1+rt )) 
Nonconstant growth valuation stockG1= 20% for 2 years; G2=5% for rest of time
D0=1.25
D1=1.25(1.20) = 1.50
D2=1.25(1.20)^{2}=1.80
D3=1.25(1.20)^{2}(1.05) =1.89
D4=1.25(1.20)^{2}(1.05)^{2}=1.98 
Internal rate of return  IRRNPV must =0 to calculate  NPV=C0 +C1 /(1+IRR)^{1}+C2 /(1+IRR)^{2}=0  Must use Excel to calculate  Pitfall 1 = Lending or borrowing?  Pitfall 2 = Multiple rates of return (when cash goes from + to )  Pitfall 3 = Mutually exclusive projects IRR sometimes ignores magnitude of a project 
Pitfall 4 – What Happens When There is More than One Opportunity Cost of Capital
Term Structure Assumption
We assume that discount rates are stable during the term of the project.
This assumption implies that all funds are reinvested at the IRR.
This is a false assumption.
Covariance of multiple stocksWith 100 securities, the box is 100 by 100.The variance terms are the diagonal terms, and thus there are 100 variance terms. The rest are the covariance terms. Because the box has(100 × 100) terms altogether, the number of covariance terms is:Number of covariance terms = 1002– 100 = 9,900Half of these terms (i.e., 4,950) are different.
bWith 50 stocks, all with the same standard deviation (.30), the same weight in the portfolio (.02), and all pairs having the same correlation coefficient (.40), the portfolio variance is
:σ2= 50(.02)2(.30)2+ [(50)2– 50](.02)2(.40)(.30)2= .03708σ = .193, or 19.3%
c.For a fully diversified portfolio, portfolio variance equals the average covariance:σ2= (.30)(.30)(.40) = .036σ = .190, or 19.0% 
  Present Value of a Growing Perpetuity
Bond ValuationPV=C1/(1+r)^{1}+C2/(1+r)^{2}...+(Par+Cn)/(1+r)^{n}  Duration = [1xPV (c1)]/PV+[2xPV (c2)]/ PV...+(TxPV(CT)]/PV  Modified Duration = volatitliy (%)=duration/(1+yield) 
DPS CalculationD0=1.50
D1=1.50(1.07)
D2=1.50(1.07)^{2}
D3=1.50(1.07)^{3}
D4=1.50(1.07)^{3}(1.05)
D5=1.50(1.07)^{3}(1.05)^{2} 
Sharpe Ratio = (rrf)/(σ)Risk premium  rrf  Standard Deviation  σ 
Ratio of risk premium to standard deviation. Measures riskadjusted performance of investment managers
SMLThe Yintercept of the SML is equal to the riskfree interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return trade off at a given time.
where:
E(Ri) is an expected return on security
E(RM) is an expected return on market portfolio M
β is a nondiversifiable or systematic risk
RM is a market rate of return
Rf is a riskfree rate
Efficient FrontierThe efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are suboptimal, because they do not provide enough return for the level of risk. 
  Stock ReturnsR=(Pt+1 Pt +D)/(Pt )  R=  Return  Pt =  Stock Price @ time  D =  Dividend 
CAPM = Capital Asset Pricing Modelri =rf +ß(rm rf )  ß=Beta  rf = risk free rate  rm = market rate  i = investment  E(r) = expected return  Expected risk premium on stock=  beta x expected risk premium on market  rrf =ß(rm rf ) 
Beta is the extent to which a stock moves with the market. CAPM says that the higher the Beta, the higher the risk
Market Efficiency1.) Weak = Market reflects past info  2.) SemiStrong = Past & Current public info is reflected  3.) All information is reflected in the stock price (public & private) 
Efficient Market  Market in which information is reflected in stock prices quickly + correctly
Profitability IndexAnother Example  continued
Proj NPV Investment PI
A 230,000 200,000 1.15
B 141,250 125,000 1.13
C 194,250 175,000 1.11
D 162,000 150,000 1.08
Select projects with highest Weighted Avg PI
WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25)
(300) (300) (300)
= 1.01
Captal RationingCapital Rationing  Limit set on the amount of funds available for investment.
Soft Rationing  Limits on available funds imposed by management.
Hard Rationing  Limits on available funds imposed by the unavailability of funds in the capital market. 
Market Risk premiumFor any investment, we can find the opportunity cost of capital using the security market line. With = 0.8, the opportunity cost of capital is:
r = rf + B(rm – rf)
r = 0.04 + [0.8 B (0.12 – 0.04)] = 0.104 = 10.4%
The opportunity cost of capital is 10.4% and the investment is expected to earn 9.8%. Therefore, the investment has a negative NPV.
If return is 11.2% What is Beta?
r = rf + (rm – rf)
0.112 = 0.04 + (0.12 – 0.04) = 0.9

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