Homework Answers
| X returns | B returns |
| -7% | 2% |
| 37% | 21% |
| -10% | 8% |
| 4% | 19% |
| 10% | 13% |
| 31% | 13% |
| 9% | 18% |
| 42% | 11% |
| 25% | 21% |
| 39% | 24% |
| -1% | 6% |
| 3% | 0% |
| -2% | 23% |
| 30% | 21% |
| 50% | -4% |
| σ(X) | σ(B) |
| 19.81% | 8.99% |
| E(Rx) | E(Rb) |
| 17.33% | 13.07% |
| Covar(X, B) | 0.00238 |
| Correlation coefficient | 0.13393 |
1.
| E(R1) = | 17.33% | sigma(R1) = | 19.81% |
| E(R2) = | 13.07% | sigma(R2) = | 8.99% |
| rho(R1,R2) = | 0.1339 | ||
| Portfolio standard deviation | Portfolio expected return | ||
| w1= | 0.1 | 8.58% | 13.49% |
| 0.2 | 8.66% | 13.92% | |
| 0.3 | 9.21% | 14.35% | |
| 0.4 | 10.16% | 14.77% | |
| 0.5 | 11.41% | 15.20% | |
| 0.6 | 12.87% | 15.63% | |
| 0.7 | 14.48% | 16.05% | |
| 0.8 | 16.19% | 16.48% | |
| 0.9 | 17.97% | 16.91% | |
| 1 | 19.81% | 17.33% |
The minimum variance portfolio of two risky assets is obtained by minimizing the Portfolio Standard Deviation by changing asset weight w1. This is done using Excel's SOLVER function.
Minimum Standard Deviation = 8.55%
Weight of Asset 1 (w1) = 0.1338 = 13.38%
Weight of Asset 2 (w2) = 1 - w1 = 0.8662 = 86.62%
2. The optimal portfolio is found in Excel through Solver. In
solver, set the objective as "to max" the Sharpe ratio, and set "by
changing variables" as asset weight w1.
| Portfolio standard deviation | Portfolio expected return | Market risk premium | Sharpe ratio | ||
| w1= | 0.211148431 | 8.70% | 13.97% | 9.82% | 1.1283 |
| 0.2 | 8.66% | 13.92% | |||
| 0.3 | 9.21% | 14.35% | |||
| 0.4 | 10.16% | 14.77% | |||
| 0.5 | 11.41% | 15.20% | |||
| 0.6 | 12.87% | 15.63% | |||
| 0.7 | 14.48% | 16.05% | |||
| 0.8 | 16.19% | 16.48% | |||
| 0.9 | 17.97% | 16.91% | |||
| 1 | 19.81% | 17.33% |
OPTIMAL PORTFOLIO (O)
Weight of Asset 1 (w1) = 0.2111 = 21.11%
Weight of Asset 2 (w2) = 1 - w1 = 0.7889 = 78.89%
Optimal Portfolio's expected return = 13.97%
Optimal Portfolio's standard deviation = 8.70%
Optimal Portfolio's Sharpe ratio = 1.1283
| Sharpe Ratio of stock X | 0.6655 |
| Sharpe Ratio of stock B | 0.9921 |
3. Slope of CAL = Shapre ratio of Optimal Portfolio = 1.1283
4. Every point on CAL represents a combination of risk-free asset (T-bill) and Optimal Portfolio with the same value of Sharpe ratio as that of Optimal Portfolio.
Composition of the Portfolio
| Stock X | Stock B | T-bill |
| 4.22% | 15.78% | 80% |
Expected return [E(R)] = Wt-bill*Rf + WO*E(RO) = 80%*4.15% + 20%*13.97% = 6.114%
Standard Deviation (σ) = WO*σO = 20%*8.70% = 1.74%
Sharpe Ratio = (6.114% - 4.15%) / 1.74% = 1.128
5. Investors looking to interpret historical returns should keep one caveat in mind: you can't assume that the future will be like the past. The older the historical return data is, the more likely it is to be less useful when predicting future returns.
As a dynamic and ever-evolving system, markets and economies at times repeat, but it is very difficult to anticipate when what's happened in the past will happen in the future. As such, you'd be hard-pressed to find financial literature that does not prominently feature the expression: past results are no indicator of future results. But euphoria and optimism prevail, and investors and their advisors erroneously put more weight on historical returns than they should.
When using historical returns, large-cap securities may exhibit more regular patterns than small cap securities. This is because large-cap securities have more liquidity than small-cap stocks.
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Please show all work. Thanks!
An optimal risky portfolio has been developed with investments in stocks and bonds This optimal portfolio has 24% invested in bonds and the remainder invested in stocks The optimal portfolio mean return is 12.05% and its standard deviation is 18.45% The t-bill rate is 4.75%; what is the mean of the complete portfolio if 33% is invested in the optimal portfolio and theremainder is invested in T-bills? a What is the resulting allocation to stocks...
Please answer(calculations) the above questions
through formulas and explain if possible. Please refrain from using
Excel functions . Thanks.
In (c) there is no need to calculate the jensen alpha.
sorry. only the sharpe ratio is needed.
University = Portfolio | Basis Bond Exercise: Finance. There are a risky assets: Assets Expected Return / X 0.75 Y I 0.7 Risk 0.2 0.4 -0.35 is the correlation between the asset returns. ca) Calculate the expected return and standard deviation of the...
The following questions are in order:
Question 1 1 pts The following data applies to Questions 1 to 3 Consider two risky assets: a stock fund and a bond fund with the following probability distributions. Scenario Severe recession Mild recession Normal growth Boom What is the expected return for the bond fund? Your answer should be in percentage points and accurate to the hundredth. For example, if your answer is 10.2511%, then type in 10.25 Probability 0.05 0.25 0.40 0.30...
Answer all questions and show work using hand formulas only. Do
NOT answer the question if you cannot answer everything.
1.
2.
3.
TABLE 5.3 Risk and return of investments in major asset classes, 1927-2016 T-bills T-bonds Stocks Arithmetic average Risk premium Standard deviation max min 3.42 N/A 3.14 14.71 -0.02 5.51 2.08 8.14 38.07 -8.47 11.91 8.48 19.99 56.38 -43.73 Using Table 5.3 as your guide, what is your estimate of the expected annual HPR on the market index...
Round Stic M Part II: Problems (50%). You MUST show me all details of your work. Simply giving me one number is NOT acceptable and receives 0, whether or the number you give is correct. 1. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of 5. The alterative risk-free investment in T-bills pays 6% per year. (15%) &. If you require a risk premium of 8%, how...
Show workings and answer to 3 decimal places thank you!
To the person who answered this question before. Dont :)
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