Risk and Returns: part 1 Economics 71a: Spring 2007 Mayo chapter 8 Malkiel, Chap 9-10 Lecture notes 3.2a

Goals  Return reminder  What is risk?  Types of risk  Statistics background  Risk return tradeoff

Returns  Total percentage gain on investment  Includes dividends for stocks  Example Price : Pays: $2 dividend Return = ( )/100 = 7%

What is Risk?  Hard question  No good answer  Statistical Features Variance/Standard deviation Histograms (probability distributions)

Types of Risk  Market  Default (financial risk)  Business  Interest rate  Liquidity  Tax  Event  Political

Statistics  Random variables and histograms  Expected returns  Variances  Covariance  Correlation

Histogram  Frequency with which random variable takes value  Gives a pictorial indication of risk  Many possible shapes  Most famous is the Normal Distribution

Random Variables and Histograms

Return Histogram

Expected Return, E(R)  N states of the world, 1, 2,..,N  pi = probability of state i  Ri = return in state i  Also called “Expected value”

Mean

Example  3 States Good: return = 20%, prob 1/4 Normal: return = 10%, prob = 1/2 Bad: return = -15%, prob = 1/4  Expected return (1/4)(20)+(1/2)(10)+(1/4)(-15)  6.25

Variance  Expected return = E(R)  Variance  Standard Deviation = Square Root (Variance)

Variance

Example  3 States Good: return = 20%, prob 1/4 Normal: return = 10%, prob = 1/2 Bad: return = -15%, prob = 1/4  Variance (1/4)( )^2+ (1/2)( )^2+ (1/4)( )^2  = Standard deviation = 12.93

Sharpe Ratio  Reward/Risk Ratio  RF = Risk free return  Relation between expected return and standard deviation or risk

Covariance and Correlation

Expectations of Linear Functions

Variances

Where do we stand?  Expected return Best probabilistic guess of what the future return will be  Variance One measure of how good that guess may turn out, or in other words, sort of a RISK measure  Histogram Complete measure of what the return could be, and RISK

Risk Versus Return  Efficient market world Return is fair payout for bearing risk Higher Risk -> Higher Return “No free lunch”  Not so efficient market world Opportunities might exist for low risk and high return Need to search these out

Idealized Risk versus Return Risk Return

Returns  Realized returns Actually returns on your investments from the past  Expected returns Mathematical forecast of future returns  Required returns Theoretically predicted return for a security given its risk level

Required Return Risk Required Return Theory prediction

Risk versus Return Efficient Market View: Investment Opportunities Risk Return * * * * * * *

Risk versus Return Not so Efficient Market View: Investment Opportunities Risk Return * * * * * * * * *

Key Questions on Risk  What is the “right” measure of risk?  How much risk do you want to bear yourself?