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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

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
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
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
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