# Expected portfolio return and risk

When we measure risk per unit of return, Repo Men, with its low expected return, becomes the most risky stock. Alta Industries is an electronics firm; Repo Men collects past-due debts; and American Foam manufactures mattresses and other foam products.

Correlation is the tendency of two variables to move together. This risk does not go away with diversification. Run a regression with returns on the stock in question plotted on the y axis and returns on the market portfolio plotted on the x axis. Note that the mean average annual return increases as the dispersion of returns increases.

Suppose an investor starts with a portfolio consisting of one randomly selected stock.

Disregard for now the items at the bottom of the data; you will fill in the blanks later. Theoretically, betas can be negative, but in the real world they are generally positive. We do not yet have enough information to choose among the various alternatives.

Regardless of the interval, the return is usually given as an annual percentage unless otherwise stated. Note that the portfolio variance decreases steadily until it reaches an asymptotic level. However, it can be used to forecast the future value of a portfolio, and it also provides a guide from which to measure actual returns.

Thus, for negative returns, the Sharpe ratio is not a particularly useful tool of analysis. Suppose some assets share some aspects of this market- wide risk, while other assets share other aspects of this market-wide risk.

Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security. Your total return from different investment options would look something like this: Therefore, investors demand a higher expected return for riskier assets.

Risk is the chance that some unfavorable event will occur. The year treasury rate at August 8, sits at 2. A security or asset beta is similar to a covariance.

This demonstrates one of the most fundamental axioms of investing: The Correlation Coefficient between the returns on two stocks can be calculated using the following equation: For a portfolio consisting of two assets, the above equation can be expressed as Expected Return on a Portfolio of Stocks A and B Note: However, remember that this return is composed of the real risk-free rate, say 3 percent, plus an inflation premium, say 5 percent.

Investors expect this additional compensation for investing in individual companies. Thus, by combining stocks into well-diversified portfolios, investors can eliminate almost one-half the riskiness of holding individual stocks.

It follows then, that the riskiness of an asset is simply the degree to which it is affected by market-wide risk. Using either the correlation coefficient or the covariance, the Variance on a Two-Asset Portfolio can be calculated as follows: Note that there are N2 cells in all, with N variances, and N2-N covariances.

Company-specific risk is generally referred to as unsystematic risk or nonsystematic risk.Assume an investment manager has created a portfolio with the Stock A and Stock B. Stock A has an expected return of 20% and a weight of 30% in the portfolio.

Stock B has an expected return. And the expected portfolio return and the portfolio variance is as follows – We know this portfolio has a risk of % with a return of %. We now move focus to 17% risk (notice the x axis), you can find two plots, one at % and another at % – what does this tell you?

Chapter 3 Risk and Return ANSWERS TO END-OF-CHAPTER QUESTIONS a.

Stand-alone risk is only a part of total risk and pertains to the It can be quite different than their expected return. f.

A risk premium is the difference between the rate of return on a The expected return on a portfolio.∧r p, is simply the weighted. However, unlike the expected return of a portfolio, the risk of a portfolio is generally not the weighted average of the standard deviation of the individual asset returns.

Only in the very rare case in which the returns of the individual assets are perfectly positively related (correlated) is a portfolio's standard deviation the weighted. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk.

This result occurs because returns on A and B are not perfectly positively correlated (ρAB = ). Chapter 5 - Page 2 Market risk premium Answer: d 4. A stock has an expected return of percent.

The beta of the stock is and the risk-free rate is 5 percent.

Expected portfolio return and risk
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