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Transcript
21.d.i Portfolio Choice In its most simplistic terms, CAPM recognizes that each portfolio will consist of some combination of riskless assets and risky assets and that an investor can choose how much to invest in each of these two types of assets. Graph 21.d.1 presented above represents a standard view of the options for riskless assets. However, the risk-reward trade-off curve for only risky assets can be seen below in Figure 21.d.2. Expected Return 0.25 0.2 0.15 0.1 K J I 0.05 H 0 0 0.1 0.2 0.3 0.4 Standard Deviation Figure 21.d.2. This is a risk-reward trade-off curve for risky assets only. The curve represents different possible risky asset portfolios. Point I is a minimum-risk point (lowest standard deviation). Points above this point trade risk for the potential for reward (expected return). Note that in reality, any risky asset portfolio on the curve that lies below point I will not ever be taken. The reason is that you are increasing your uncertainty while reducing your expected return, which is ludicrous. Now one can combine the two graphs presented above to find the risk-reward combinations that can be obtained by combining riskless assets with risky assets. Figure 21.d.3 represents all possible combinations for both risky and riskless asset portfolios. More importantly, it shows that there will be an optimal combination portfolio. This point lies at the tangency between the two curves. 0.25 Expected Return 0.2 F 0.15 D 0.1 C J B A 0.05 I E G K H 0 0 0.1 0.2 Standard Deviation 0.3 0.4 Figure 21.d.3. This shows the optimum combination of risky assets and riskless assets. Points D and J are equivalent and exist as tangency points between the two curves. This is known as the preferred portfolio for the theoretical relationships between expected return and standard deviation for risky and riskless assets. Note that the CAPM does not allow for investors to choose the makeup of the bundle of risky assets that are held. They can only choose how much of this bundle they will hold relative to their holdings of risk-less assets. The reason for this is as follows. The CAPM asserts that in equilibrium an investor’s relative holdings of risky assets will be the same as the market portfolio, which holds all risky assets in proportion to their observed market values. Its composition is based upon the supply of existing assets, whose relative worth are assessed at current market prices. This bundle of risky assets – the market portfolio (a risky asset portfolio) – is then the most efficient bundle and therefore offers the highest possible expected rate of return at a specified level of risk. This is visualized on a graph just as the point D/J on graph 21.d.3, only one does not have to choose that bundle of risky assets corresponding to a tangency on the riskless asset line (straight line) because it is put upon the investor as the only realistically efficient risky asset bundle. Based upon the results in figure 21.d.3, the possible preferred portfolios – consisting of some riskless assets and some amount of the market portfolio bundle, together totaling 100% of investments – lie between points A and D on what can now be called the Capital Market Line (CML) This is depicted as the green line in figure 21.d.4. 0.25 Expected Return 0.2 F 0.15 D 0.1 C J B A 0.05 I E G K H 0 0 0.1 0.2 0.3 0.4 Standard Deviation Figure 21.d.4. Show the possible preferred combination portfolios on the green line up to and including the market portfolio – point D. Point A is only riskless asset investment. All points between A and D are some combination of market portfolio holdings and riskless asset holdings. For example, point B appears on the graph as 33 1/3 % market portfolio and 66 2/3 % riskless assets (the closer you are to point A the more riskless assets you have). CML Formula: E(r) = rf + E (rm ) r f m Where rf is the expected return for riskless assets (.04), r m is the expected return for the market portfolio (.1), and σm is the expected standard deviation of the market portfolio. E(r) and σ are the expected rates of return and standard deviation for the preferred portfolio. Again, consisting of both the market portfolio of risky assets and the riskless assets. The following is a graphical explanation of why the market portfolio is the best choice as the risky asset component of the total preferred portfolio. It is depicted in figure 21.d.5 on the next page. σ of portfolio return total risk nonsystematic risk σm systematic risk # of security holdings Figure 21.d.5. Total risk is composed of both nonsystematic risk (blue line) and systematic risk (orange line). σm is the standard deviation of the market. You can see that as one increases their security holdings, thus approaching the market portfolio (increase number of security holdings), they will rid themselves of all nonsystematic risk – security specific risk. Since systematic risk – market risk – is always there, you cannot get rid of it. So the goal is to minimize as much risk as possible, and that only includes nonsystematic risk. This is called diversification and is one of the principles of the CAPM, which is why it assumes that all investors will choose the market portfolio for their risky asset component. We have now established how to choose a preferred portfolio, which will be unique to each investors risk tolerance, temporal position, etc. However, every preferred portfolio will consist of some combination of not only riskless asset, but also risky asset – form the market portfolio. Some Problems: 1. According to the CAPM, a simple method for an investor to create his or her optimal portfolio (what I have been calling preferred) is to: a.) invest in riskless asset b.) invest in self-selected risky assets as well as riskless asset c.) invest in only self-selected risky assets d.) invest in some combination of the market portfolio with risk0free asset 2. An investor has a risk aversion equal to the average investor in the market. Market investors hold Honda and Pepsi stock in the proportion of 1:3. If the above investor has $100,000 to spend on a portfolio, how much will he spend for Pepsi and Honda stock, respectively? a.) $10,000/$90,000 b.) $25,000/$75,000 c.) $75,000/$25,000 d.) none of the above 3. Given the following: expected rate of return on riskless assets of .05; expected rate of return on the market of .15; standard deviation of the market portfolio of .2. What is the CML line and what is the reward to risk ratio? a.) E(r) = .15 + .5σ; .15 b.) E(r) = .05 + .5σ; .5 c.) E(r) = .15 + .05σ; .05 d.) E(r) = .05 + .5σ; .05 Answers: d, b, b