Portfolio Management and Investment Analysis

Classified in Economy

Written at December 4, 2024 on English with a size of 5.47 KB.

1. Volatility of Returns

- Small company stocks

2. Christine's Return

P0= $42.40, P1= $38.20, Divd= 1.4%

- [(38.20-42.4)/42.4] + 0.014 = -8.51%

3. Scott's Annual Return

200 shares, P0= $48, n= 4 months, dividend= $0.22

HPR= -0.120

- Annual return= (1-0.120417)^(12/4)-1 = -31.95%

4. Annualized Return

Annual returns: 15%, 12%, -18%, 2%, 37%, n=5

- Standard deviation= 20.03%

5. Stock Return Range

Stock return= 14.6%, standard deviation= 19.2%, two-thirds of the time?

- -4.6% to 33.8%

6. Forecasting Returns

Historical dollar-weighted... If you want to forecast, the best:

- Arithmetic average return

7. Jeanette's Future Value

Investment= $12,000, n=4, arithmetic average= 8.72%, geometric average= 8.43%

- FV= 12,000(1+0.0843)^4 = $16,587

8. Black Stone's Geometric Average Return

Returns: 9%, 16%, -7%, 13%

- Geometric average= [(1+0.09)(1+0.16)(1-0.07)(1+0.13)]^(1/4) - 1= 7.36%

9. Dollar-Weighted Average Return

Rates of return for a risky portfolio...

- Dollar-weighted average= 0.74%

10. Investment Allocation

Investment= $10,000. Risky asset --> Return= 15%, standard deviation= 21%; T-Bill --> Return=5%. How much money should be invested in the risky asset for an expected return of 11%?

11%= (15%*r)+(5%*(1-r)) --> r= 60%

- 10,000*0.6 = $6,000

11. Portfolio Expected Return and Standard Deviation

70% in risky asset (return=15%, variance=0.05) + 30% in T-Bill (return=5%).

- E(r)= 0.70.15 + 0.30.05= 12%

- Standard deviation= 0.7 * (0.05)^(1/2) = 15.7%

12. Sharpe Measure

Standard deviation= 25%, Beta= 1.3, return= 15%, T-bills paying at 4.5%.

- (15-4.5)/25= 0.42

13. Degree of Risk Aversion

- Determines the optimal mix of the risk-free asset and optimal risky asset

14. Diversification Effectiveness

- Most effective when security returns are negatively correlated

15. Diversification Benefits

- Can be achieved as long as the correlation between securities is less than 1

16. Portfolio Standard Deviation

A --> standard deviation= 35%

B --> standard deviation= 15%

Correlation = 0.45, A= 40%, B= 60%.

- Portfolio standard deviation= 19.76%

17. Missing Information

18. Minimum Variance Portfolio

Stock standard deviation= 18%, Bond standard deviation= 11%. Correlation=0.24%.

- Approximate weight of stock fund in minimum variance portfolio= 21%

19. Zero Volatility Portfolio

Stock Boom and Stock Bust are perfectly negatively correlated. Their standard deviations are 24.495% and 9.798% respectively.

- Approximate weight of Stock Boom for a zero-volatility portfolio= 28%

20. Optimal Risky Portfolio

Risky portfolio:

A --> E(r)= 21%, standard deviation= 39%

B --> E(r)= 14%, standard deviation= 20%

Correlation=0.4, risk-free rate= 5%.

- Proportion of the optimal risky portfolio invested in B= 71%

21. Tobin's Separation Property

- Portfolio choice can be separated into two independent tasks: identifying the optimal risky portfolio and constructing a complete portfolio based on the investor's degree of risk aversion.

22. Portfolio Beta

Jonathan: (A 25%; 0.78), (B 40%; 0.85), (C 35%; 1.7)

- Portfolio Beta= 1.13

23. CAPM Beta

CAPM, risk-free rate= 5%, market return= 15%, E(r)= 12%

E(r)= risk-free rate + Beta(market return - risk-free rate)

- Beta= 0.7

24. CAPM and Fairly Priced Securities

- Fairly priced securities have zero alphas

25. Security Valuation with CAPM

Security X: expected return= 13%, beta= 1.5

- Security X is overpriced according to CAPM.

26. Excess Return

- The difference between the rate of return earned and the risk-free rate.

27. Security Market Line (SML)

- III and IV: Investors should accept any return located above the SML line. A beta of 0.0 indicates the risk-free rate of return.

28. Risk-Free Rate Calculation

Stock X: Beta=0.87, E(r)= 9.8%. Stock Y: Beta= 1.2, E(r)= 13.1%.

- Risk-free rate= 1.10%

29. Beta Calculation

Standard deviation of stock= 22.4%, covariance with market= 0.0169. Market standard deviation= 13.2%.