QUESTION
Exhibit 1
| Alex Sharpe’s Portfolio | |||
| Exitbit 1. Investment Return Data | |||
| Date | S&P 500 | RJR | Hasbro |
| Jan-02 | -1.70% | 6.13% | 1.66% |
| Feb-02 | -2.31% | 9.87% | -13.27% |
| Mar-02 | 4.37% | -1.37% | 10.55% |
| Apr-02 | -5.06% | 6.87% | 1.01% |
| May-02 | -1.19% | 2.17% | -4.26% |
| Jun-02 | -7.15% | -23.97% | -11.37% |
| Jul-02 | -8.23% | 1.64% | -9.66% |
| Aug-02 | 0.64% | 7.71% | 7.35% |
| Sep-02 | -10.64% | -31.48% | -15.36% |
| Oct-02 | 7.35% | 0.57% | -8.18% |
| Nov-02 | 5.96% | -4.81% | 25.44% |
| Dec-02 | -5.50% | 9.09% | -9.91% |
| Jan-03 | -2.46% | 0.59% | 3.90% |
| Feb-03 | -1.72% | -5.78% | 0.92% |
| Mar-03 | 0.89% | -19.17% | 14.70% |
| Apr-03 | 8.12% | -12.68% | 15.19% |
| May-03 | 6.18% | 21.02% | 0.06% |
| Jun-03 | 1.48% | 9.15% | 9.24% |
| Jul-03 | 2.18% | -4.54% | 7.78% |
| Aug-03 | 2.34% | -3.86% | -1.86% |
| Sep-03 | -1.06% | 15.78% | 0.97% |
| Oct-03 | 5.89% | 21.47% | 16.70% |
| Nov-03 | 1.51% | 14.93% | 1.42% |
| Dec-03 | 4.39% | 5.34% | -3.75% |
| Jan-04 | 2.20% | 1.56% | -7.19% |
| Feb-04 | 1.40% | 4.52% | 10.73% |
| Mar-04 | -1.20% | -1.99% | -0.55% |
| Apr-04 | -2.56% | 7.06% | -13.15% |
| May-04 | 1.24% | -13.23% | 4.08% |
| Jun-04 | 2.00% | 20.27% | -3.36% |
| Jul-04 | -3.88% | 6.45% | -4.37% |
| Aug-04 | 0.11% | 4.93% | 1.98% |
| Sep-04 | 1.91% | -9.88% | 1.46% |
| Oct-04 | 1.66% | 1.21% | -5.90% |
| Nov-04 | 4.43% | 9.83% | 7.57% |
| Dec-04 | 3.34% | 3.93% | 1.84% |
| Jan-05 | -2.74% | 2.32% | 1.14% |
| Feb-05 | 2.09% | 1.90% | 7.76% |
| Mar-05 | -1.86% | -1.66% | -3.17% |
| Apr-05 | -2.66% | -3.25% | -7.48% |
| May-05 | 3.59% | 6.34% | 6.66% |
| Jun-05 | 0.99% | -4.96% | 3.02% |
| Jul-05 | 4.22% | 5.72% | 5.53% |
| Aug-05 | -0.78% | 0.76% | -5.65% |
| Sep-05 | 0.93% | -1.10% | -5.07% |
| Oct-05 | -2.19% | 2.38% | -4.12% |
| Nov-05 | 3.82% | 4.73% | 8.39% |
| Dec-05 | 0.19% | 7.09% | -1.18% |
| Jan-06 | 3.90% | 6.08% | 5.05% |
| Feb-06 | -0.36% | 4.96% | -4.29% |
| Mar-06 | 1.76% | -0.61% | 3.99% |
| Apr-06 | 1.15% | 3.93% | -6.59% |
| May-06 | -3.30% | 0.26% | -5.94% |
| Jun-06 | -0.19% | 4.88% | -2.32% |
| Jul-06 | -0.28% | 9.96% | 3.26% |
| Aug-06 | 2.30% | 2.65% | 8.56% |
| Sep-06 | 1.81% | -4.76% | 12.07% |
| Oct-06 | 3.60% | 1.92% | 13.93% |
| Nov-06 | 2.13% | 1.71% | 3.20% |
| Dec-06 | 0.91% | 1.91% | 1.87% |
ANSWER
1
Risk is a complicated criterion and its measure changes with the context. Generally, we use the standard deviation of a stock to measure the risk associated with the stock. A higher standard deviation would indicate that the stock is riskier to invest in. But, the perspective changes as we change the context from an individual stock to a portfolio. A stock which is risky standalone might be a perfect addition to a portfolio and even reduce the overall risk associated with the portfolio.
A portfolio consists of multiple stocks and it is the interaction of the stocks within a portfolio that finally decide the overall risk associated with any portfolio. The final aim that a portfolio looks at is its overall diversification against the market portfolio and still keep the returns at an optimum level which are acceptable to the investors. The portfolio will aim to add stocks from different sectors and industries within the sectors to increase the diversity of the portfolio. As we add different stocks the chances of all the component stocks tanking at the same time decreases. In a perfectly diversified portfolio only the systematic risk of the market remains, and the individual risks of the companies/stocks are countered by the other stocks.
The metric we look at for diversity is correlation. The lower the correlation of the component stocks the better it is for the portfolio (a negative correlation is even better). Thus, an individual stock might have a very high standard deviation but if its correlation to a portfolio is negative or low then its addition to the portfolio can be fruitful for the portfolio and contribute to the reduction of its risk.
We can see the same effect in part b and part c as well where when accounted for individually Reynolds had a higher standard deviation than Hasbro and for a single stock investment Reynolds would have been a riskier decision. But when we see the correlation of Reynolds and Hasbro with the portfolio of S&P 500, we realise that the correlation of Reynolds is lower with the index when compared to Hasbro. Thus, addition of Reynolds actually decrease the overall risk of the portfolio and thereby makes our portfolio more diversified. The decision is even better as the return of Reynolds is higher than that of Hasbro which further escalates the returns of our original portfolio.
The right measure of the stock is still the standard deviation of the stock, but we have to also account for a few other aspects like the return of the stock and the context in which the discussion of risk is being assessed. A higher return is generally accompanied by a higher risk. Also, if the high risk increases the diversity the overall risk reduces.
2
|
S&P 500 |
RJR |
Hasbro |
|
|
Average Monthly Return |
0.566% |
1.875% |
1.184% |
|
Standard Deviation |
3.60% |
9.29% |
8.05% |
The Average monthly returns and the standard deviation of Reynolds, Hasbro and the S&P 500 index are calculated using the average and standard deviation (population) function of excel.
We can see that Reynolds have a higher standard deviation than Hasbro and thus it appears to be riskier than Hasbro. However, at the same time we should be cognisant of the fact that return of Reynolds is also higher than Hasbro. The return risk ratio is higher for Reynolds when compared to Hasbro and thus, it does compensate in returns what it demands in terms of the added risk of investment.
3
a)
The results using the realised returns column is as follows:
|
1% Reynolds |
1% Hasbro |
|
|
Average Monthly Return |
0.579% |
0.572% |
|
Standard Deviation |
3.59% |
3.61% |
For calculating the realised returns, we took the return of S&P 500 index as 99% by weight and 1% weight was given to the stock. The mathematical formula of the same is as follows:
Realised Returns = 0.99*return of S&P 500 + 0.01* Return of the selected stock
b)
The correlation of the selected tocks with S&P 500 are as follows:
|
RJR |
Hasbro |
|
|
Correlation |
0.2892406 |
0.6303892 |
The return of the portfolio is calculated using the following formula:
Average Monthly Return = 0.99* average monthly return of S&P 500 +
0.01* average monthly return of the selected stock
The standard deviation is calculated using the following formula:
Standard Deviation = SQRT(0.992* square of standard deviation of S&P 500
+ 0.012* square of standard deviation of selected stock
+ 0.99*0.01*correlation coefficient*standard deviation of S&P 500
* standard deviation of selected stock
The calculated results are as follows:
|
1% Reynolds |
1% Hasbro |
|
|
Average Monthly Return |
0.579% |
0.572% |
|
Standard Deviation |
3.58% |
3.59% |
The obtained results are not exactly the same as those obtained in part 1. The average returns will always be the same using both the methods however the standard deviations might differ. There is compounding effect of the monthly returns which is captured by the realised returns column. The same cannot be captured by the average returns and standard deviation before portfolio is made. The difference, however, does not generally change the ranking of different combinations in terms of risk. There is only a small margin of difference but there is a difference, nonetheless.
Based on the portfolios made Hasbro looks riskier. The change from part 2 to part three is due to the inclusion of the correlation of the stocks with the index. Reynolds has very less correlation with S&P 500 index whereas Hasbro has 60% correlation with the index. Thus, Reynolds adds to the diversification of our original portfolio much more when compared to Hasbro. Thus, Reynolds will be a les risky addition. We also see that the standard deviation of the portfolio actually decreases on adding Reynolds to the portfolio.
Exhibit 1
| Alex Sharpe’s Portfolio | |||||||
| Exitbit 1. Investment Return Data | |||||||
| Date | S&P 500 | RJR | Hasbro | 1% Reynolds | 1% Hasbro | ||
| Jan-02 | -1.70% | 6.13% | 1.66% | -1.62% | -1.67% | ||
| Feb-02 | -2.31% | 9.87% | -13.27% | -2.19% | -2.42% | ||
| Mar-02 | 4.37% | -1.37% | 10.55% | 4.31% | 4.43% | ||
| Apr-02 | -5.06% | 6.87% | 1.01% | -4.94% | -5.00% | ||
| May-02 | -1.19% | 2.17% | -4.26% | -1.16% | -1.22% | ||
| Jun-02 | -7.15% | -23.97% | -11.37% | -7.32% | -7.19% | ||
| Jul-02 | -8.23% | 1.64% | -9.66% | -8.13% | -8.24% | ||
| Aug-02 | 0.64% | 7.71% | 7.35% | 0.71% | 0.71% | ||
| Sep-02 | -10.64% | -31.48% | -15.36% | -10.85% | -10.69% | ||
| Oct-02 | 7.35% | 0.57% | -8.18% | 7.28% | 7.19% | ||
| Nov-02 | 5.96% | -4.81% | 25.44% | 5.85% | 6.15% | ||
| Dec-02 | -5.50% | 9.09% | -9.91% | -5.35% | -5.54% | ||
| Jan-03 | -2.46% | 0.59% | 3.90% | -2.43% | -2.40% | ||
| Feb-03 | -1.72% | -5.78% | 0.92% | -1.76% | -1.69% | ||
| Mar-03 | 0.89% | -19.17% | 14.70% | 0.69% | 1.03% | ||
| Apr-03 | 8.12% | -12.68% | 15.19% | 7.91% | 8.19% | ||
| May-03 | 6.18% | 21.02% | 0.06% | 6.33% | 6.12% | ||
| Jun-03 | 1.48% | 9.15% | 9.24% | 1.56% | 1.56% | ||
| Jul-03 | 2.18% | -4.54% | 7.78% | 2.11% | 2.24% | ||
| Aug-03 | 2.34% | -3.86% | -1.86% | 2.28% | 2.30% | ||
| Sep-03 | -1.06% | 15.78% | 0.97% | -0.89% | -1.04% | ||
| Oct-03 | 5.89% | 21.47% | 16.70% | 6.05% | 6.00% | ||
| Nov-03 | 1.51% | 14.93% | 1.42% | 1.64% | 1.51% | ||
| Dec-03 | 4.39% | 5.34% | -3.75% | 4.40% | 4.31% | ||
| Jan-04 | 2.20% | 1.56% | -7.19% | 2.19% | 2.11% | ||
| Feb-04 | 1.40% | 4.52% | 10.73% | 1.43% | 1.49% | ||
| Mar-04 | -1.20% | -1.99% | -0.55% | -1.21% | -1.19% | ||
| Apr-04 | -2.56% | 7.06% | -13.15% | -2.46% | -2.67% | ||
| May-04 | 1.24% | -13.23% | 4.08% | 1.10% | 1.27% | ||
| Jun-04 | 2.00% | 20.27% | -3.36% | 2.18% | 1.95% | ||
| Jul-04 | -3.88% | 6.45% | -4.37% | -3.78% | -3.88% | ||
| Aug-04 | 0.11% | 4.93% | 1.98% | 0.16% | 0.13% | ||
| Sep-04 | 1.91% | -9.88% | 1.46% | 1.79% | 1.91% | ||
| Oct-04 | 1.66% | 1.21% | -5.90% | 1.66% | 1.58% | ||
| Nov-04 | 4.43% | 9.83% | 7.57% | 4.48% | 4.46% | ||
| Dec-04 | 3.34% | 3.93% | 1.84% | 3.35% | 3.33% | ||
| Jan-05 | -2.74% | 2.32% | 1.14% | -2.69% | -2.70% | ||
| Feb-05 | 2.09% | 1.90% | 7.76% | 2.09% | 2.15% | ||
| Mar-05 | -1.86% | -1.66% | -3.17% | -1.86% | -1.87% | ||
| Apr-05 | -2.66% | -3.25% | -7.48% | -2.67% | -2.71% | ||
| May-05 | 3.59% | 6.34% | 6.66% | 3.62% | 3.62% | ||
| Jun-05 | 0.99% | -4.96% | 3.02% | 0.93% | 1.01% | ||
| Jul-05 | 4.22% | 5.72% | 5.53% | 4.24% | 4.23% | ||
| Aug-05 | -0.78% | 0.76% | -5.65% | -0.76% | -0.83% | ||
| Sep-05 | 0.93% | -1.10% | -5.07% | 0.91% | 0.87% | ||
| Oct-05 | -2.19% | 2.38% | -4.12% | -2.14% | -2.21% | ||
| Nov-05 | 3.82% | 4.73% | 8.39% | 3.83% | 3.87% | ||
| Dec-05 | 0.19% | 7.09% | -1.18% | 0.26% | 0.18% | ||
| Jan-06 | 3.90% | 6.08% | 5.05% | 3.92% | 3.91% | ||
| Feb-06 | -0.36% | 4.96% | -4.29% | -0.31% | -0.40% | ||
| Mar-06 | 1.76% | -0.61% | 3.99% | 1.74% | 1.78% | ||
| Apr-06 | 1.15% | 3.93% | -6.59% | 1.18% | 1.07% | ||
| May-06 | -3.30% | 0.26% | -5.94% | -3.26% | -3.33% | ||
| Jun-06 | -0.19% | 4.88% | -2.32% | -0.14% | -0.21% | ||
| Jul-06 | -0.28% | 9.96% | 3.26% | -0.18% | -0.24% | ||
| Aug-06 | 2.30% | 2.65% | 8.56% | 2.30% | 2.36% | ||
| Sep-06 | 1.81% | -4.76% | 12.07% | 1.74% | 1.91% | ||
| Oct-06 | 3.60% | 1.92% | 13.93% | 3.58% | 3.70% | ||
| Nov-06 | 2.13% | 1.71% | 3.20% | 2.13% | 2.14% | ||
| Dec-06 | 0.91% | 1.91% | 1.87% | 0.92% | 0.92% | ||
| S&P 500 | RJR | Hasbro | 1% Reynolds | 1% Hasbro | |||
| Average Monthly Return | 0.566% | 1.875% | 1.184% | Average Monthly Return | 0.57909% | 0.57218% | |
| Standard Deviation | 3.60% | 9.29% | 8.05% | Standard Deviation | 3.59% | 3.61% | |
| RJR | Hasbro | ||||||
| Correlation | 0.289240571214592 | 0.630389224829131 | |||||
| 1% Reynolds | 1% Hasbro | ||||||
| Average Monthly Return | 0.579% | 0.572% | |||||
| Standard Deviation | 3.58% | 3.59% |
Looking for best Finance Assignment Help. Whatsapp us at +16469488918 or chat with our chat representative showing on lower right corner or order from here. You can also take help from our Live Assignment helper for any exam or live assignment related assistance.