10.4 The Efficient Set for Two Assets
Our results for expected returns and standard deviations are graphed in Figure 10.2. The figure shows a dot labeled Slowpoke and a dot labeled Supertech. Each dot represents both the expected return and the standard deviation for an individual security. As can be seen, Supertech has both a higher expected return and a higher standard deviation. The box or "El" in the graph represents a portfolio with 60 percent invested in Supertech and 40 percent invested in Slowpoke. You will recall that we previously calculated both the expected return and the standard deviation for this portfolio. The choice of 60 percent in Supertech and 40 percent in Slowpoke is just one of an infinite number of portfolios that can be created. The set of portfolios is sketched by the curved line in Figure 10.3.

Figure 10.2
Expected Returns a n d Standard Deviations for Supertech, Slowpoke, a n d a Portfolio Composed o f 60 Percent i n Supertech a n d 40 Percent i n Slowpoke

Expected return (%)

Supertech

b

Slowpoke

I

I

I

I

11.50

15.44

25.86

Standard deviation (%)

Figure 10.3
Set of Portfolios c o m p o s e d of Holdings in Supertech and Slowpoke (correlation between the t w o securities i s -0.1639)

Expected return on portfolio (%)

I
I

Slowpoke
I

Standard deviation of portfolio's return (%) Portfolio 1is composed of 90 percent Slowpoke and 10 percent Supertech (p = -0.1639). Portfolio Zis composed of 50 percent Slowpoke and 50 percent Supertech (p = -0.1639). Portfolio 3is composed of 10 percent Slowpoke and 90 percent Supertech (p = -0.1639). Portfolio l ' i s composed of 90 percent Slowpoke and 10 percent Supertech (p = 1). Point MY denotes the minimum variance portfolio. This is the portfolio with the lowest possible variance. By definition, the same portfolio must also have the lowest possible