PORTFOLIO THEORY
Risk & Return
 Return over Holding Period
 Return over multiple periods
 Arithmetic Mean
 Geometric Mean
 Dollar Averaging or IRR
 Return of investments has some uncertainty
 Scenario Analysis
Risk & Return & Normal Distribution
 Random Variable
 Mean
 Standard Deviation
 Correlation
 Normal Distribution
Risk Premium and Risk Aversion
 Risk Free Rate
 Risk Aversion
 Risk Premium
 Speculation vs Gambling
 Price of Risk
 Market Price of Risk
 Sharpe Ratio (Reward-to-Volatility) Ratio
Inflation and Real Rate of Return
 Nominal Interest Rate (growth rate of economy)
 Real Interest Rate (growth rate of purchasing power)
 Real Rate ≈ Nominal Rate – Inflation
r≈R–i
(1+r)(1+i) = (1+R)
r = (R – i)/(1+i)
 R = r + E(i)
Capital Allocation Line
 Consider only two assets: Risk Free and Risky
 Let rf be risk free rate
 Let S be a be a risky asset with expected return of rs and
risk of σs
 Capital should be allocated along Capital Allocation Line
depending on the risk tolerance of investor
 Assuming assets are fairly priced, the portfolio will be a
combination of risk and riskless.
 ETF has made the above easy
Diversification
 Two types of risk:
 Market Risk, Systemic Risk, Nondiversifiable Risk that
impact the whole economy
 Unique risk, Firm Specific Risk, Diversifiable Risk that is
specific to the asset
 Diversification helps reduce specific risk
Diversification
 Diversification using two assets
 Diversification using many assets
 Single-Index Stock Market
 Regression Y = a + bX
 R=α+βM+e
 e is uncorrelated with M hence
 Var(R) = β2 Var(M) + Var(e)
 β > 1 Cyclical
 β <1 Defensive