Investments Midterm 2 PDF

Ch 7: Optimal Risky Portfolios Diversification should reduce portfolio risk. All securities are affected by common macroeconomic factors. For example, if all stocks are affected by the business cycle, we cannot avoid exposure to business cycle risk no matter how many s...

Ch 7: Optimal Risky Portfolios Diversification should reduce portfolio risk. All securities are affected by common macroeconomic factors. For example, if all stocks are affected by the business cycle, we cannot avoid exposure to business cycle risk no matter how many stocks we hold. When all risk is firm-specific, diversification can reduce risk to arbitrarily low levels. With all risk sources independent, the exposure to any particular source of risk is reduced to a negligible level. Insurance Principle: reducing risk by spreading exposure across many independent risk sources is sometimes called the The portfolio standard deviation falls as the number of securities increases, but it cannot be reduced to zero. The risk that remains even after extensive diversification is called market risk, also called systematic risk. The risk that can be eliminated by diversification is called unique risk, firm-specific risk, non-systematic risk, or diversifiable risk. Efficient diversification constructs risky portfolios to provide the lowest possible risk for any given level of expected return. The first step is to determine the risk-return opportunities available to the investor. These are summarized by the minimum-variance frontier of risky assets. Second, we identify the optimal portfolio of risky assets by finding the portfolio weights that result in the steepest CAL. Finally, we choose an appropriate complete portfolio by mixing the risk-free asset with the optimal risky portfolio. Before describing the process in detail, let us first present an overview. For any portfolio on the lower portion of the minimum-variance frontier, there is a portfolio with the same standard deviation and a greater expected return positioned directly above it. Hence the bottom part of the minimum-variance frontier is inefficient. The CAL generated by the optimal portfolio, P, is the one tangent to the efficient frontier. This CAL dominates all alternative feasible lines. The principal idea behind the frontier set of risky portfolios is that, for any risk level, we are interested only in that portfolio with the highest expected return. Alternatively, the frontier is the set of portfolios that minimizes the variance for any target expected return. Harry Markowitz in 1952, Modern Portfolio Theory holds that a given investment's risk and return characteristics should not be viewed in isolation; rather, it should be judged according to how it affects the overall portfolio's risk and return You can either: Maximize the return associated with a given level of risk Minimize the level of risk associated with a given return The return on a stock comes in two forms:  The capital gain (the difference between the selling price and purchase price) The Dividends paid by the company Portfolios that satisfy this optimal mix of stocks are said to lie along the efficient frontier. Diversification is not unlimited. Beyond a certain point adding more stocks will cease to have an appreciable effect on the portfolio’s risk. For the level of risk to fall the stocks in the portfolio must be uncorrelated. If instead they tend to rise and fall together, diversification offers no advantage. We refer to the risk we have diversified away as the company or unique risk The risk that remains is market risk. Ch 6: Capital Allocation to Risky Assets History shows us that long-term bonds have been riskier investments than Treasury bills and that stocks have been more dangerous still. Riskier investments have offered higher average returns. The most straightforward way to control the risk of the portfolio is through the fraction of the portfolio invested in Treasury bills or other safe money market securities versus what is invested in risky assets. ( have no standard deviation or risk) The most basic asset allocation choice: How much of the portfolio should be placed in risk-free money market securities versus other risky asset classes? When we shift wealth from the risky portfolio to the risk-free asset, we do not change the relative proportions of the various risky assets within the risky portfolio. Rather, we reduce the relative weight of the risky portfolio as a whole in favour of risk-free assets. We do not alter the weights of each security within the risky portfolio, the probability distribution of the rate of return on the risky portfolio remains unchanged by the asset reallocation. What will change is the probability distribution of the rate of return on the complete portfolio that consists of the risky asset and the risk-free asset. Capital allocation line (CAL): It depicts all the risk-return combinations available to investors. The slope of the CAL denoted S, equals the increase in the expected return of the complete portfolio per unit of additional standard deviation- in other words, incremental return per incremental risk. Ch 8: Index Models The success of a portfolio selection rule depends on the quality of the input list, that is, the estimates of expected security returns and the covariance matrix. In the long run, efficient portfolios will beat portfolios with less reliable input lists and consequently inferior reward-to-risk trade-offs. We, therefore, will decompose the sources of return uncertainty into uncertainty about the economy as a whole, which is captured by a systematic market factor that we will call m and uncertainty about the firm in particular, which is captured by a firm-specific random variable that we will call e;.m is a common factor affects all securities The common dependence that virtually all firms have to macroeconomic conditions is the source of the correlation between their security returns. The S&P 500 is a valid proxy for the common macroeconomic factor.  This approach leads to an equation similar to the single-factor model, which is called a single-index model because it uses the market index to proxy for the common factor. The intercept of this equation (denoted by the Greek letter alpha, or O'.) is the security's expected excess return when the market excess return is zero. The slope coefficient is the security beta. Beta is the security's sensitivity to the index. It is the amount by which the security return tends to increase or decrease for every 1% increase or decrease in the return on the index. Ch 9: CAPM The CAPM model was published 12 years later in articles by William Sharpe, John Lintner, and Jan Mossin. The CAPM is based on two sets of assumptions. The first set pertains to investor behaviour and allows us to assume that investors are alike in the most important ways, specifically that they are all mean-variance optimizers with a common time horizon and a common set of information reflected in their use of an identical input list. T The second set of assumptions pertains to the market setting, asserting that markets function well with few impediments to trading. Even a cursory consideration of these assumptions reveals that they are fairly strong, and one may justifiably wonder whether a theory derived from them will withstand empirical tests. Each investor uses an input list (expected returns and covariance matrix) to draw an efficient frontier employing all available risky assets and identifies an efficient risky portfolio, P, by drawing the tangent CAL (capital allocation line) to the frontier. Assumptions l(a) (investors are all mean-variance optimizers), 2(a) (all assets trade and therefore can be held in investors' portfolios), and 2(b) (investors can borrow or lend at the risk-free rate and therefore can select portfolios from the capital allocation line of the tangency portfolio). The CAPM asks what would happen if all investors shared an identical investable universe and used the same. Because the market portfolio is the aggregation of all of these identical risky portfolios, it too will have the same weights. The mutual fund theorem is if all investors would freely choose to hold a common risky portfolio identical to the market portfolio, they would not object if all stocks in the market were replaced with shares of a single mutual fund holding that market portfolio. The expected return-beta relationship tells us that the total expected rate of return is the sum of the risk-free rate (compensation for waiting, i.e., the time value of money) plus a risk premium (compensation for worrying, specifically about investment returns). The difference between the fair and expected rates of return on a stock is called the stock's alpha  It is the product of a benchmark risk premium (that of the broad market portfolio) and the relative risk of the particular asset as measured by its beta, portrayed by the SML. The CAPM is also useful in capital budgeting decisions. For a firm considering a new project, the CAPM can provide the required rate of return that the project needs to yield, based on its beta, to be acceptable to investors.