(i) The restrictions of 40 equities are more likely to increase the risk of the portfolio. It may be a small increase in risk. It can be caused due to the lack of diversification with a comparison withholding 80-100 equities in the portfolio. There are same correlations between each pair of equities, as well as the standard deviation of the 100 equities. The formula of equal-weighted portfolio variance shown below:
σ2= variance
ρ= correlation coefficient
ρσ2 = covariance among the each pair of equities
There is a small sign if there is a change in n in the second term of the formula above. For an example, assume that ρ= 0.3 and σ=34%, we could calculate the variance with a result of 3.55% and standard deviation of 18.84% with 100 equities, and would increase to a variance of 3.67% and standard deviation of 19.16% when there are only 40 equities. An increase in the variance of 0.12%, standard deviation 0.32%, and it is reasonable to be accepted if there is a sufficient expected return.
(ii) Ross will curb an increase in risk by ensuring that the remaining 40 issues in the portfolio are retained with a fair diversification. It also includes a weak correlation between the issues that are remained. As mentioned in (a), there is only a small increase in risk. This indicates that Roses has to focus on only a few industries and also diversify its portfolio of investment to many industries. It will lead to a greater correlation between the issues.
The risk reduction benefits of diversification are no longer a linear feature of the number of issues in the portfolio. On the contrary, if you have the lowest degree of diversification, the incremental benefits from other diversification are the most important. By limiting Ross to 20 rather than 40 issues are riskier to increase the portfolio than reducing the size of the portfolio from 60 stocks to 40 stocks. As the example given above, limiting to 20 issues will cause the standard deviation to increase to 19.69%, by a 0.53% increase in standard deviation resulting from holding 20 of 40 stocks is greater than the 0.32% increase that results from holding 40 of 100 stocks.
As Ross’ portfolio is a portion of the 7 portfolios (one seventh), which is 14.29 % of the aggregate investment, restricting the holdings of Ross’ portfolio to either 20 or 40 issues has only a small effect on the fund of aggregate investment. It may be advantageous due to the fact Ross had outperformed for the past 5 to 6 years, and he is skilfully in stock picking.
Question 2
Investors may always overvalue the growth stocks’ profits and dividends. They may also be undertaking recent increase to a way into the future, thereby underestimating the inevitable slowdown. Boom stocks are probably to convert to lower average returns, whilst value stocks might also convert to greater average returns in any given time, typically in a longer time horizon in the future.
In an efficient markets, the relevant information has been displayed by the stocks’ current price. In this circumstance, either boom or value stocks provide the same expected return.
Question 3
For the equation of constant-growth dividend discount model shown below:
V_0=D/(k-g)
where the greater the dividends, the greater the price of equity with the assumption of a constant dividend growth rate. For example, if the company increases the dividend payout rate, a decrease in the growth rate g will occur. At the same time, return on equity may not be constant, and if the return on equity(ROE) is greater than the market capitalization rate(k), the price of equity will fall. In this situation, the director might be confused.
As the dividend payout increase, the sustainable growth rate will be reduced. For the equation of growth rate (g) given below:
g=b×ROE
where b =plowback ratio
Blowback ratio, indicated how much profits are earned after the paid out dividends, and it can be calculated using the formula shown below:
b=((Earnings-Dividends) )/(Total Earnings)
From this equation, we can see that a greater dividend payout will cause a reduction in plowback ratio as fewer funds are reinvested, which would cause a lower growth rate.
(ii) As the dividend payout increase, the book value growth rate will be reduced. As dividend payout increase will lead to fewer funds reinvested. Thus, the book value will be reduced.
Question 4
Each bond has a maturity of five years. We assume that coupons are paid annually, and both bonds are sold at face value. If there is a drop of yield from 8% declines to 7%, the value of the Amex bond will increase to RM104.10. The price of the Goggle bond will rise, but at most, it will not exceed the call price of RM101. The present value of scheduled payments is greater than RM101, but the call price sets an upper limit for the actual bond price.
If there is a decline in the interest rate, the Amex bond will be more attractive because it is not subject to call, its potential capital gains will be greater. If rates are expected to rise, Goggle is a relatively better investment. Its higher coupon and higher yield to maturity will provide a higher rate of return than the Amex bond.