Ch: 11- Return and Risk: CAPM

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Ch: 11- Return and Risk: CAPM. Realized return Expected Return Individual Security Risk Covariance and Correlation Portfolio Expected Returns Diversification Effect Portfolio Risk and CAPM. Realized Return. Investors earn returns from stocks in two forms: Dividends, Capital gains

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Ch: 11- Return and Risk: CAPM

Realized return

Expected Return

Individual Security Risk

Covariance and Correlation

Portfolio Expected Returns

Diversification Effect

Portfolio Risk and CAPM

Realized Return
• Investors earn returns from stocks in two forms: Dividends, Capital gains
• Realized Return in dollars = Dividend + (Price1 – Price0)
• Rate of Realized Return = Dividend yield + Capital yield
• R = (D/P0) + (P1-P0)/P0 = (D + P1 – P0)/P0
• Another name for realized return is “Holding period return”
Expected Return
• Expected return is the average return an investor can expect from a stock in the future
• List all the possible returns and find their average to calculate expected return
• This example suggests that all the possible outcomes have equal chance of happening
• If not then probability of each occurrences have to be found and assigned as weights.
• Weighted average of the individual returns would give the expected return
Individual Security Risk
• There is uncertainty over expected rate
• This uncertainty is the risk of the stock
• Risk is measured by variance and standard deviation.
• Measure of how much the return will change or deviate from the expected
• Variance = Standard Deviation squared
Covariance and Correlation
• The relationship between return of one stock with the other can be measured with: Covariance and correlation
• Negative values for both measures means the returns are opposite to each other
• Positive values for both measures mean the returns are similar or close to each other.
• Correlation ranges in between -1 & 1, whereas covariance can be of any value
Portfolio Expected Return
• In Summary:
• What happens if an investor invests in both these companies and create a portfolio of investment?
Portfolio Expected Return
• If an investor who has \$100 invests \$60 in supertech and the rest in slowpoke then what is the portfolio expected return he will earn?
• R = [(60/100) X 17.5] + [(40/100) X 5.5]

= 12.7%

• Expected portfolio return is the weighted average of the individual stocks’ returns. The weights are based on the portion of total investment in each stock
Diversification Effect
• Weighted Average Standard Deviation =

(0.6 X 0.2586) + (0.4 X 0.115) = 20.12%

• Unlike expected return, the risk of a portfolio is not the weighted average of the individual stocks’ risks.
• The weighted average calculation does not take into account the covariance and correlation in between the stocks.
• Whenever a portfolio is created there is a diversification effect due to the correlation.
Diversification Effect
• Negative correlation of two stocks mean when one is giving negative return the other is giving positive return and vice versa.
• Thus a portfolio of the two stocks will minimize the risk of loss as the positive stock will cover the losses of the negative stock
• This is the diversification effect of a portfolio
Diversification Effect
• Systematic and Unsystematic Risk:
• Systematic Risk is any risk that affects a large number of assets, each to a greater or lesser degree.
• Macroeconomic risks associated with the entire market
• Cannot be minimized through diversification
• Unsystematic Risk is a risk that specifically affects a single asset or a small group of assets
• Stand-alone risk due to the specific news and information available about an asset.
• Measured with Variance and Standard Deviation
• Can be completely removed through diversification
Portfolio Risk and CAPM
• Unsystematic risk can be removed through addition of more stocks
• So, Standard Deviation of portfolio is unimportant since it can be zero with enough number of shares
• Systematic Risk is the only risk associated with a portfolio and it is the only one an investor should be worried about
• Can be measured with Beta.
Portfolio Risk and CAPM
• Beta is a ratio of change in market return with changes in stock’s return
Portfolio Risk and CAPM

Slope of a graph with Return on Stock at X-axis and Return on Market in Y-axis is the Beta for the stock.

OR

The following formula can also be used to find Beta:

Portfolio Risk and CAPM
• Return from any asset should be able to compensate for all risks, through risk premiums, and still make profit.
• Thus R = Profit + Risk Premium
• Profit is the return at risk-free rate that can be achieved from a security without any risk
• For bond returns Rb = Rf + RPb
• For stock market return Rm = Rf + RPm
• For an individual stock return Rs = Rf + RPs
Portfolio Risk and CAPM
• Since systematic risk is the only risk associated with a stock that needs compensation, and that risk depends on the market’s risk
• Thus RPs = β X RPm
• OR RPs = β X (Rm – Rf)
• Therefore, Rs = Rf + β(Rm – Rf)
• This is the Capital Asset Pricing Model (CAPM) used to find the required return of a stock.
• When required return equals expected return market is said to be at equilibrium