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

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Ch 11 return and risk capm

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

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

  • 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

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

Individual security risk1

Individual Security Risk

Covariance and correlation

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

Covariance and correlation1

Covariance and Correlation

Portfolio expected return

Portfolio Expected Return

  • In Summary:

  • What happens if an investor invests in both these companies and create a portfolio of investment?

Portfolio expected return1

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

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 effect1

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 effect2

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

Diversification effect3

Diversification Effect

Portfolio risk and capm

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 capm1

Portfolio Risk and CAPM

  • Beta is a ratio of change in market return with changes in stock’s return

Portfolio risk and capm2

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.


The following formula can also be used to find Beta:

Portfolio risk and capm3

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 capm4

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

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