3 Students often confuse the SML in Figure 1111 with line in Figure 119

# 3 students often confuse the sml in figure 1111 with

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3. Students often confuse the SML in Figure 11.11 with line in Figure 11.9 . Actually, the lines are quite different. Line traces the efficient set of portfolios formed from both risky assets and the riskless asset. Each point on the line represents an entire portfolio. Point is a portfolio composed entirely of risky assets. Every other point on the line represents a portfolio of the securities in combined with the riskless asset. The axes on Figure 11.9 are the expected return on a and the standard deviation of a . Individual securities do not lie along line . The SML in Figure 11.11 relates expected return to beta. Figure 11.11 differs from Figure 11.9 in at least two ways. First, beta appears in the horizontal axis of Figure 11.11 , but standard deviation appears in the horizontal axis of Figure 11.9 . Second, the SML in Figure 11.11 holds both for all individual securities and for all possible portfolios, whereas line in Figure 11.9 holds only for efficient portfolios. We stated earlier that, under homogeneous expectations, point in Figure 11.9 becomes the market portfolio. In this situation, line is referred to as the capital market line (CML). Summary and Conclusions This chapter set forth the fundamentals of modern portfolio theory. Our basic points are these: 1. This chapter showed us how to calculate the expected return and variance for individual securities, and the covariance and correlation for pairs of securities. Given these statistics, the expected return and variance for a portfolio of two securities and can be written as: 2. In our notation, stands for the proportion of a security in a portfolio. By varying we can trace out the efficient set of portfolios. We graphed the efficient set for the two-asset case as a curve, pointing out that the degree of curvature or bend in the graph reflects the diversification effect: The lower the correlation between the two securities, the greater the bend. The same general shape of the efficient set holds in a world of many assets. 3. Just as the formula for variance in the two-asset case is computed from a 2×2 matrix, the variance formula is computed from an × matrix in the -asset case. We showed that with a large number of assets, there are many more covariance terms than variance terms in the matrix. In fact the variance terms are effectively diversified away in a large portfolio, but the covariance terms are not. Thus, a diversified portfolio can eliminate some, but not all, of the risk of the individual securities. 4. The efficient set of risky assets can be combined with riskless borrowing and lending. In this case a rational investor will always choose to hold the portfolio of risky securities represented by point in Figure 11.9 . Then he can either borrow or lend at the riskless rate to achieve any desired point on line in the figure.

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