Risk And Rate Of Returns In Financial Management

Risk and Rates of Return ,[object Object],[object Object],[object Object]

Investment returns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is investment risk? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Probability distributions ,[object Object],[object Object],Expected Rate of Return Rate of Return (%) 100 15 0 -70 Firm X Firm Y

Selected Realized Returns, 1926 – 2001 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Investment alternatives Economy Prob. T-Bill HT Coll USR MP Recession 0.1 8.0% -22.0% 28.0% 10.0% -13.0% Below avg 0.2 8.0% -2.0% 14.7% -10.0% 1.0% Average 0.4 8.0% 20.0% 0.0% 7.0% 15.0% Above avg 0.2 8.0% 35.0% -10.0% 45.0% 29.0% Boom 0.1 8.0% 50.0% -20.0% 30.0% 43.0%

Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? ,[object Object],[object Object],[object Object],[object Object]

How do the returns of HT and Coll. behave in relation to the market? ,[object Object],[object Object]

Return: Calculating the expected return for each alternative

Summary of expected returns for all alternatives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Risk: Calculating the standard deviation for each alternative

Standard deviation calculation

Comparing standard deviations USR Prob. T - bill HT 0 8 13.8 17.4 Rate of Return (%)

Comments on standard deviation as a measure of risk ,[object Object],[object Object],[object Object],[object Object]

Comparing risk and return * Seem out of place. Security Expected return Risk, σ T-bills 8.0% 0.0% HT 17.4% 20.0% Coll* 1.7% 13.4% USR* 13.8% 18.8% Market 15.0% 15.3%

Coefficient of Variation (CV) ,[object Object]

Risk rankings, by coefficient of variation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Illustrating the CV as a measure of relative risk ,[object Object],0 A B Rate of Return (%) Prob.

Investor attitude towards risk ,[object Object],[object Object]

Portfolio construction: Risk and return ,[object Object],[object Object],[object Object]

Calculating portfolio expected return

An alternative method for determining portfolio expected return Economy Prob. HT Coll Port. Recession 0.1 -22.0% 28.0% 3.0% Below avg 0.2 -2.0% 14.7% 6.4% Average 0.4 20.0% 0.0% 10.0% Above avg 0.2 35.0% -10.0% 12.5% Boom 0.1 50.0% -20.0% 15.0%

Calculating portfolio standard deviation and CV

Comments on portfolio risk measures ,[object Object],[object Object],[object Object],[object Object]

General comments about risk ,[object Object],[object Object],[object Object]

Returns distribution for two perfectly negatively correlated stocks ( ρ = -1.0) -10 15 15 25 25 25 15 0 -10 Stock W 0 Stock M -10 0 Portfolio WM

Returns distribution for two perfectly positively correlated stocks ( ρ = 1.0) Stock M 0 15 25 -10 Stock M’ 0 15 25 -10 Portfolio MM’ 0 15 25 -10

Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio ,[object Object],[object Object],[object Object]

Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Company-Specific Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

Breaking down sources of risk ,[object Object],[object Object],[object Object]

Failure to diversify ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Capital Asset Pricing Model (CAPM) ,[object Object],[object Object]

Beta ,[object Object],[object Object]

Calculating betas ,[object Object],[object Object]

Illustrating the calculation of beta . . . k i _ k M _ - 5 0 5 10 15 20 20 15 10 5 -5 -10 Regression line: k i = -2.59 + 1.44 k M ^ ^ Year k M k i 1 15% 18% 2 -5 -10 3 12 16

Comments on beta ,[object Object],[object Object],[object Object],[object Object]

Can the beta of a security be negative? ,[object Object],[object Object],[object Object]

Beta coefficients for HT, Coll, and T-Bills k i _ k M _ - 20 0 20 40 40 20 -20 HT: β = 1.30 T-bills: β = 0 Coll: β = -0.87

Comparing expected return and beta coefficients ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Security Market Line (SML): Calculating required rates of return ,[object Object],[object Object],[object Object]

What is the market risk premium? ,[object Object],[object Object],[object Object]

Calculating required rates of return ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Illustrating the Security Market Line . . Coll. . HT T-bills . USR SML k M = 15 k RF = 8 -1 0 1 2 . SML: k i = 8% + (15% – 8%) β i k i (%) Risk, β i

An example: Equally-weighted two-stock portfolio ,[object Object],[object Object],[object Object],[object Object],[object Object]

Calculating portfolio required returns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Factors that change the SML ,[object Object],SML 1 k i (%) SML 2 0 0.5 1.0 1.5 18 15 11 8  I = 3% Risk, β i

Factors that change the SML ,[object Object],SML 1 k i (%) SML 2 0 0.5 1.0 1.5 18 15 11 8  RP M = 3% Risk, β i

Verifying the CAPM empirically ,[object Object],[object Object],[object Object]

More thoughts on the CAPM ,[object Object],[object Object],[object Object]

Risk And Rate Of Returns In Financial Management

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Risk And Rate Of Returns In Financial Management