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Amount from the separate investment scheme at the 25th year,
Assuming 52 weeks in a year,
Let P1 be the principal (deposit less down payment). At the end of year three,
Principal required between years three to year five,
Principal required between years five to year eight,
Principal required between years eight to year ten,
I first need to deposit a sum of 200000 for down payment followed by a principle of 104604.43 at the beginning of the first year to the end of the third year. At the end of year three, I should withdraw a sum of to remain with a balance of 83 050.53 at the beginning of 4th year. At the end of year 5, I need to deposit additional to my account to achieve a principle of 251050.64 at the beginning of the 6th year. Finally, I should deposit an additional at the end of year 8 to achieve a principle 1081387.07 at the beginning of 9th year for the period up to the end of the 10th year.
Hence, the total amount deposited, as discussed above, over the entire period is,
Since the Coupon payments are semi- annual,
c) When the interest rate is 11.5%, the bond value becomes less than the face value – an implication that the bond is discounted for on sale. The value of the bond increases as the time to maturity approaches below the coupon rate.
When the interest rate is below the Coupon rate i.e. at 6%, the value of the bond lowers with the approaching maturity time.
The values of the historical returns for each of the portfolios and assets described in part II of the question are as tabulated below:
Expected return is the return that an individual expects a stock to earn over the next period while risk is the measure of deviation of the actual return from the expected return.
Risk is indicated by:
i. Variance – measure of the squared deviations of a security’s return from its expected return.
ii. Standard deviation – square root of variance.
Best portfolio is indicated by a high value of expected return and a low risk while worst portfolio is that which the value of the expected return is low and risk is high i.e. an inverse relationship exists between the expected return and risk
Diversification is the strategy of creating a portfolio with more than a single investment in order to reduce the risk associated with any one investment and to increase the chances of making profits.
Diversification minimizes risks and boosts the expected returns.
The statistical relationship between the multiple securities that constitute a portfolio is indicated by the correlation coefficient. Diversification benefits are accrued if the securities in a portfolio are perfectly negatively correlated. In case of positive correlation, minimal diversification benefits are accrued.
With reference to table 1, multiple combinations of different securities have been used to create the alpha, beta and gamma portfolios. This minimizes the risks associated with a single investment such as one purely investing in shares then in a particular year the company experiences profit fall.
Systematic risk component of an asset is measured using Beta (β).
Asset B will be more volatile than the market compared to asset A. This is because a beta value of greater than 1 offers a chance of higher rate of capital return hence more risk while β<1 provides lower returns and consequently lower risks.
Effects of changes in the market on the systematic risk component of an asset
In case of increase in the market value of the asset by 10%, company A with β=0.5 would provide a 5% gain for the company while a market return of -10% would provide a return of -5% (a loss of 5%) to the company.
Similarly, company B with β=2 would expectedly provide a double market return i.e. an increment in the market return by 10% would imply an additional 20% gain/profits for the company while a decrement in the market return by 10% would provide an additional return of
-20% (a loss of 20%) to the company.
Risk aversion is the tendency to prefer less risk to greater risk for a given value of expected return or to prefer less returns with known risks at the expense of greater returns with unknown risks.
Within the different stages of ‘investing life cycle’, risk aversion is mainly associated with the young and the less wealthy part of the population who prefer investing in securities such as government bonds because of the less risks/losses associated with them.
Plot of historical returns of each portfolio versus the years
Fig 1.1: A plot of historical returns of the alpha portfolio against the years
Fig 1.2: A plot of historical returns of the Beta portfolio against the years
Fig 1.3 A plot of historical returns of the Gamma portfolio against the years
From the plots, best portfolio for each of the customer is as summarized in the table below:
Portfolio of Preference
A young Deakin commerce graduate (Stephanie) with a long and successful career ahead of her.
A middle aged couple (Harold and Meredith) who are high income earners. They plan to retire in 10 years.
An older member of the workforce (Akhter) who is hoping to retire in the next 18 months.
Justifications for the choices made
Case I: Since Stephanie is young, she would prefer investment option with less risk (risk aversion). Therefore, Stephanie would invest a larger proportion of her wealth in securities such as bonds due to the less risk associated with it. The best portfolio option for her is thus Portfolio γ.
Case II: Because the Harold and Meredith are duo and high income earners, the best investment for them is that associated with the highest risk which comes along with the greatest returns. They would not suffer great impact in case of a loss as they have 10 more years to work and generate the high income. Hence, the best portfolio for them is Portfolio α.
Case III: Due to the fast approaching retirement age, Akhter should invest in a portfolio with medium risks hence medium profits. Being that he is old, he incurs minimal expenses hence he can make good use of his medium profits. The best option for him is thus Portfolio β.
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