Investments
Investment returns are the amount that the investment is worth (upon sale), net of taxes, over and above the price paid for the investment. The returns can be expressed either in absolute terms, or in annualized terms. The return on an investment that cost $1,000 and is sold for $1,060 a year later is as follows:
Open
Close
Return
% Return
This graph shows that the odds of an outcome increase as the expected return approaches 6%. If there were an infinite number of scenarios, the graph would look like this, but the tails on the y axis would by fully extended infinitely as the probability of an outcome approaches zero.
The expected rate of return on the Treasury bonds is the weighted average of the probabilities and returns listed in the table. Thus:
Probability
Return
W.Avg
-14
-1.4
-4
-0.8
Expected Return
The expected return therefore is 6% on the Treasury bond.
d. Stand-alone risk reflects the risk associated with a single asset. In the portfolio, stand-alone risk reflects the undiversified risk of any one individual asset (Investopedia, 2015). The standard deviation of the bond's expected return for the next year is as follows:
Probability
Return
W.Avg
0.1
-14
-1.4
0.2
-4
-0.8
0.4
6
2.4
0.2
16
3.2
0.1
26
2.6
6
2.130728
The standard deviation is 2.13.
e. The standard deviation of Blandy's returns over the past ten years is as follows:
e.
26
15
-14
-15
2
-18
42
30
-32
28
25.193
Standard Deviation
The standard deviation of the returns for Blandy is 25.193.
f. The client should be surprised that I would recommend reducing risk by purchasing a stock with even more risk than Blandy has. The returns of this portfolio over the past ten years would have been as follows:
Year
Blandy
Gourmange
Combined
1
26
47
31.25
2
15
-54
-2.25
3
-14
15
-6.75
4
-15
7
-9.5
5
2
-28
-5.5
6
-18
40
-3.5
7
42
17
35.75
8
30
-23
16.75
9
-32
-4
-25
10
28
75
39.75
Avg
6.4
9.2
7.1
Std Dev
25.19
38.58
Correlation is the degree to which two things are related. In investments, correlation specifically refers to the degree to which two assets move together. The estimated correlation between Blandy and Gourmange is:
g.
Year
Blandy
Gourmange
1
26
47
2
15
-54
3
-14
15
4
-15
7
5
2
-28
6
-18
40
7
42
17
8
30
-23
9
-32
-4
10
28
75
0.1125
Correlation
The correlation between Blandy and Gourmange is 0.1125. This means that the returns of these two securities are very poorly correlated with each other. This is the reason why the standard deviation of the combined portfolio is lower than the standard deviation of either asset individually -- the movements of one are typically offset by the movements of the either. Because the two assets have a low correlation, diversifying with these two will lower the overall standard deviation of the portfolio.
h. As a general rule, each random stock added to the portfolio will reduce its standard deviation. The portfolio's risk will thus decrease with each added stock. . This is because each added stock decreases the amount of firm-specific risk that the portfolio has, until enough stocks have been added than only systemic risk remains. The movements of the individual stocks will offset each other, when there are enough stocks, such that the portfolio's returns approach the market returns.
i. Portfolio effects should influence how investors think about the risk of individual stocks. The above example shows why -- the overall portfolio risk was lowered by adding a stock with higher volatility. Thus, it is not the risk associated with the individual asset that matters so much as the way that adding that asset affects the risk of the portfolio overall. If you have a one-stock portfolio, you would not necessarily be compensated for that. You are exposed to more risk, and consequently could expect greater returns, but on a risk-adjusted basis you would not have any real reason to expect superior returns. So even when you earn a risk premium, you have paid for that premium anyway -- returns are relative to the risk undertaken to earn them.
j. In CAPM, the beta measures the risk that an individual asset has. The beta is the correlation between the asset's returns and the overall market returns. The closer correlated to the broad market that an asset is, the closer to 1.00 will be the beta. So in CAPM, the beta represents the firm specific risk, which is added to the overall market risk,…
