Consider an economy with two types of firms, S and I. S firms all move together. I firms move independently. For both types of firms, there is a 59 % probability that the firm will have a 24 % return and a 41 % probability that the firm will have a - 20 % return. What is the volatility (standard deviation) of a portfolio that consists of an equal investment in:
a. 36 firms of type S?
b. 36 firms of type I?
E(R) = p1 x R1 + p2 x R2 = 59% x 24% + 41% x (-20%) = 5.96%
Variance, V = p1 x [R1 - E(R)]2 + p2 x [R2 - E(R)]2 = 59% x (24% - 5.96%)2 + 41% x (-20% - 5.96%)2 = 0.0468318
Hence, standard deviation = SD = V1/2 = (0.04683184)1/2 = 0.216406654 = 21.64%
Part (a)
Since, S firms all move together, hence there will be no benefit of diversification and hence the standard deviation of a portfolio that consists of an equal investment in 36 firms of type S = SD = 21.64%
Part (b)
I firms move independently. The stocks are uncorrelated.
Hence, the standard deviation of a portfolio that consists of an equal investment in 36 firms of type I
= SD / n1/2 = 21.64% / (36)1/2 = 3.61%
Consider an economy with two types of firms, S and I. S firms all move together....
Consider an economy with two types of firms, S and I. S firms
all move together. I firms move independently. For both types of
firms, there is a 60% probability that the firms will have a 15%
return and a 40% probability that the firms will have a −10%
return. What is the volatility (standard deviation) of a portfolio
that consists of an equal investment in 20 firms of (a) type S, and
(b) type I?
My Question: Finding Standard...
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 50% probability that the firm will have a 20% return and a 50% probability that the firm will have a -30% return. The standard deviation for the return on an portfolio of 20 type S firms is closest to:
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 20% probability that the firm will have a 20% retum and a 80% probability that the firm will have a - 30% retum. The standard deviation for the return on an individual firm is closest to: O A. 8% OB. 10% O C. 20% OD. -20%
A. -5 %
B. 5.59%
C. 12.5%
D. 25%
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 50% probability that the firm will have a 20% return and a 50% probability that the firm will have a - 30% return. The standard deviation for the return on a portfolio of 20 type | firms is closest...
4. Suppose that a stock gave a realized return of 20% over a two-year time period and a 10% return over the third year. The geometric average annual return is ________. (2 points) A) 8.28% B) 12.43% C) 14.08% D) 16.57% 5. Bear Stearns' stock price closed at $98, $103, $58, $29, $4 over five successive weeks. The weekly standard deviation of the stock price calculated from this sample is ________. (2 points) A) $30.07 B) $49.40 C) $42.96 D)...
Consider the following information: State of Economy Probability of State of Economy Rate of Rtn Stock A Rate of Rtn Stock B Rate of Rtn Stock C Boom .20 .24 .45 .33 Good .35 .09 .10 .15 Poor .30 .03 -.10 -.05 Bust .15 -.05 -.25 -.09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio?...
Consider the following information on a portfolio of three stocks Probability of State of State of Stock A Stock B Stock C Economy Rate of Return Rate of Return Rate of Return Economy 14 Boom 03 .33 .59 Normal 54 11 13 21 Bust .32 17 -12 -36 a. If your portfolio is invested 38 percent each in A and B and 24 percent in C, what is the portfolio's expected return, the variance, and the standard deviation? (Do not...
(a) Suppose that the CAPM holds. Consider stocks A, B, C and D
plotted in the graph below together with portfolios X, T (the
tangency or market portfolio), Z, and the risk-free asset S. No
explanation necessary.
(i) If you could invest in the risk-free asset S and only one of
the stocks A, B, C or D, which stock would you choose?
(ii) Which of the stocks, A, B, C, or D, has the highest
beta?
(iii) Which of...
Consider an investment with the following payoffs and probabilities: State of the economy Probability Return GDP grows slowly .40 1,000 GDP grows fast .60 2,000 What is the expected value? What is the standard deviation of the investment? (.40) (1,000) + (.60) (2,000) = 400+1200=1600 Standard deviation= 10,000,000 2 =3162.27 How do I get he standard deviation?
2. The standard deviation of a probability distrubution measures how bunched together the data is. The larger the standard deviation, the further away from the mean the data tends to be. Consider the two density functions below: 1 P1(c) 2-12,000 2 (3,204 e 1 2-22,000 e 10) 3, 204721 P2(x) 9) 12,060727 Suppose that these give the density functions for the return on investment for two different invest- ment options. Say we have two investment firms with different investing philosophies:...