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Risk And Return Of Security And Portfolio
 

Risk And Return Of Security And Portfolio

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    Risk And Return Of Security And Portfolio Risk And Return Of Security And Portfolio Presentation Transcript

    • Risk and Return
    • Holding Period Return
      • Three month ago, Peter Lynch purchased 100
      • shares of Iomega Corp. at $50 per share. Last
      • month, he received dividends of $0.25 per
      • share from Iomega. These shares are worth
      • $56 each today.
      • Compute Peter’s holding period return from his investment in Iomega common shares.
    • Probability Concept
      • Random variable
        • Something whose value in the future is subject to uncertainty.
      • Probability
        • The relative likelihood of each possible outcome (or value) of a random variable
        • Probabilities of individual outcomes cannot be negative nor greater than 1.0
        • Sum of the probabilities of all possible outcomes must equal 1.0
      • Moments
        • Mean, Variance (or Standard deviation), covariance
    • Computing the Basic Statistics A security analyst has prepared the following probability distribution of the possible returns on the common stock shares of two companies: Compu-Graphics Inc. (CGI) and Data Switch Corp. (DSC).
    • The Mean For CGI, the mean (or expected) return is: Similarly, the mean return for DSC is 24.00%
    • The Variance and Standard Deviation The variance of CGI’s returns is: The Standard Deviation of CGI’s return is:
    • The Covariance The covariance of the returns on CGI and DSC is:
    • The Correlation Coefficient The correlation coefficient between CGI and DSC is:
    • Summary of Results for CGI and DSC
      • A portfolio is a combination of two or more securities.
      • Combining securities into a portfolio reduces risk.
      • An efficient portfolio is one that has the highest expected return for a given level of risk.
      • We will look at two-asset portfolios in fair detail.
      Portfolio Securities
    • Portfolio Expected Return and Risk Expected Return Risk The Expected Returns of the Securities The Portfolio Weights The Risk of the Securities The Portfolio Weights The Correlation Coefficients
    • Portfolio Weights and Expected Return
    • Portfolio Expected Return and Risk
    • Diversification of Risk
      • Note that while the expected return of the portfolio is between those of CGI and DSC, its risk is less than either of the two individual securities.
      • Combining CGI and DSC results in a substantial reduction of risk - diversification!
      • This benefit of diversification stems primarily from the fact that CGI and DSC’s returns are not perfectly correlated .
      • All else being the same, lower the correlation coefficient, lower is the risk of the portfolio.
        • Recall that the expected return of the portfolio is not affected by the correlation coefficient.
      • Thus, lower the correlation coefficient, greater is the diversification of risk.
      Correlation Coefficient and Portfolio Risk
    • Consider stocks of two companies, X and Y. The table below gives their expected returns and standard deviations . Plot the risk and expected return of portfolios of these two stocks for the following (assumed) correlation coefficients: -1.0 0.5 0.0 +0.5 +1.0 Correlation Coefficient and Portfolio Risk
    • Correlation Coefficient and Portfolio Risk Y Correlation Coefficient -1.0 -0.5 0.0 +0.5 +1.0 X
    • Portfolios with Many Assets
      • The above framework can be expanded to the case of portfolios with a large number of stocks.
      • In forming each portfolio, we can vary
        • the number of stocks that make up the portfolio,
        • the identity of the stocks in the portfolio, and
        • the weights assigned to each stock.
      • Look at the plot of the expected returns versus the risk of these portfolios
    • All Combinations of Risky Assets
    • Efficient Frontier
      • A portfolio is an efficient portfolio if
        • no other portfolio with the same expected return has lower risk, or
        • no other portfolio with the same risk has a higher expected return.
      • Investors prefer efficient portfolios over inefficient ones.
      • The collection of efficient portfolio is called an efficient frontier .
    •  (risk) Efficient Frontier  (expected return) F E
    • Choosing the Best Risky Asset
      • Investors prefer efficient portfolios over inefficient ones.
      • Which one of the efficient portfolios is best?
      • We can answer this by introducing a riskless asset .
        • There is no uncertainty about the future value of this asset (i.e. the standard deviation of returns is zero). Let the return on this asset be r f .
        • For practical purposes, 90-day U.S. Treasury Bills are (almost) risk free.
    • Combinations of a Risk Free and a Risky Asset  (risk)  (expected return) F E N r f
    • Best Risky Asset  (expected return)  (risk) F E M r f
    • The Capital Market Line
      • Assume investors can lend and borrow at the risk free rate of interest.
        • borrowing entails a negative investment in the riskless asset.
      • Since every investor hold a part of the “best” risky asset M, M is the market portfolio.
      • The Market portfolio consists of all risky assets.
        • Each asset weight is proportional to its market value.
    • The Capital Market Line Sharpe Ratio
    • The Capital Market Line r f  (expected return)  (risk) F E M
      • Explain the importance of asset pricing models.
      • Demonstrate choice of an investment position on the Capital Market Line (CML).
      • Understand the Capital Asset Pricing Model (CAPM), Security Market Line (SML) and its uses.
      Next Coverage
      • Understand the determination of the expected rate of return  Capital Asset Pricing Model
      • Decomposition of Risk: Systematic Vs. Unsystematic.
    • Asset Pricing Models
      • These models provide a relationship between an asset’s required rate of return and its risk .
      • The required return can be used for:
        • computing the NPV of your investment.
    • Individual’s Choice on the CML  (risk)  (risk)
    • The Capital Asset Pricing Model (CAPM)
      • It allows us to determine the required rate of return (=expected return) for an individual security.
        • Individual securities may not lie on the CML.
        • Only efficient portfolios lie on the CML
      • The Security Market Line ( SML ) can be applied to any securities or portfolios including inefficient ones.
    • The Security Market Line (SML)
      • where
    • What does the SML tell us
      • The required rate of return on a security depends on:
        • the risk free rate
        • the “beta” of the security, and
        • the market price of risk.
      • The required return is a linear function of the beta coefficient.
        • All else being the same, higher the beta coefficient, higher is the required return on the security.
    • Graphical Representation of the SML
    • Computing Required Rates of Return
      • Common stock shares of Gator Sprinkler Systems (GSS) have a correlation coefficient of 0.80 with the market portfolio, and a standard deviation of 28%. The expected return on the market portfolio is 14%, and its standard deviation is 20%. The risk free rate is 5%.
      • What is the required rate of return on GSS?
    • Required Return on GSS First compute the beta of GSS: Next, apply the SML:
    • Required Rate of Return on GSS
      • What would be the required rate of return on GSS if it had a correlation of 0.50 with the market? (All else is the same)
        • Beta = 0.70 and  GSS = 11.30%
      • What would be the required rate of return on GSS if it had a standard deviation of 36%, and a correlation of 0.80? (All else is the same)
        • Beta = 1.44 and  GSS = 17.96%
    • Estimating the Beta Coefficient
      • If we know the security’s correlation with the
      • market, its standard deviation, and the standard
      • deviation of the market, we can use the
      • definition of beta:
      • Generally, these quantities are not known.
      • We therefore rely on their historical values to provide us with an estimate of beta.
    • Interpreting the Beta Coefficient The beta of the market portfolio is always equal to 1.0. The beta of the risk free asset is always equal to 0.0
    • Interpreting the Beta Coefficient
      • Beta indicates how sensitive a security’s returns are to changes in the market portfolio’s return .
        • It is a measure of the asset’s risk.
      • Suppose the market portfolio’s risk premium is +10% during a given period.
        • if  = 1.50, the security’s risk premium will be +15%.
        • if  = 1.00, the security’s risk premium will be +10%
        • if  = 0.50, the security’s risk premium will be +5%
        • if  = - 0.50, the security’s risk premium will be - 5%
    • Beta Coefficients for Selected Firms
    • Beta of a Portfolio
      • The beta of a portfolio is the weighted average of the beta values of the individual securities in the portfolio.
      • where w i is the proportion of value invested in security i, and  i is the beta of the security i.
    • Applying the CAPM
      • The CML prescribes that investors should invest in the riskless asset and the market portfolio.
      • The true market portfolio, which consists of all risky assets, cannot be constructed.
      • How much diversification is necessary to get substantially “all” of the benefits of diversification?
        • About 25 to 30 stocks!