Part 1
1-What is the intuition behind the construction of a three-stage dividend discount model?
The intuition on which the three-stage dividend discount model is based is that the growth rate of the dividends can change for more than one year during the entire life of the share stock. As per this model, the assumption is that the dividends will change twice, and the model is based on three growth rates of the dividends that perpetuate the stock value during its life.
2-What, if any, is the link between the no-growth value per share and the present value of growth opportunities (PVGO)?
The price of a stock is equal to the Present value of growth opportunities plus the no-growth value per share. Thus, for any company, the difference between the no-growth value per share and the actual value or price of the stock is equal to its present value of the growth opportunities.
V_0=E/r+ PVGO
Here,
E/r is the no-growth value per share
PVGO is the Present Value of Growth Opportunities
And
V0 is the Value or Price of the stock
Part 2
3-You have a $60 million equity portfolio with a Beta of 1.5, and appropriate equity futures are trading at 2300 (Full Price) and have a Beta of .99.
What futures trade would be required to reduce the overall beta of your portfolio to .8?
The futures contracts are the standardized tools that have default minimum risk and aid in reducing the counterparty risk as well as it uses the central clearing houses. The futures can be used for the purpose of hedging and managing the risk by changing and modifying the underlying characteristics of the portfolio. This is done by changing the overall payoff of the total position of the futures and the portfolio as per a given movement in the market. Futures are quite liquid and are easily shorted and are also less expensive than other instruments. This makes them an ideal derivative for hedging or managing portfolio risk. Therefore, using a future, the following needs to be done to reduce the risk or beta value of the overall portfolio:
The company could short sell:
= ((1.5-0.8)×$6000000)/(2300 )=4200000/2300 =1826 contracts
The company could short sell 1826 contracts to reduce the overall portfolio beta to 0.8.
4-Tyler is a portfolio manager for an unconstrained bond fund and has a portfolio that totals $475 million. Tyler’s overall bond allocation is 60% and the Fixed Income portfolio has an overall duration of 8. Tyler is worried about interest rates increasing over the next few months and wants to lower the duration of his fixed income holdings. Since Tyler’s Fund is unconstrained, it is hard to find an appropriate derivative contract that matches his portfolio, therefore, his hedged portfolio is subject to increased basis risk.
Tyler found a derivative Fixed Income futures contract that trades for $215,000 (full price, including multiplier) that has an overall effective duration of 2. Also, Tyler has adjusted for the mismatch of his portfolio with the duration and has a calculated a yield beta of 1.5 for the derivative contract with the holdings in his portfolio.
What futures trade would be required to reduce the portfolio’s fixed income holdings to have an effective duration of 3?
In terms of fixed-income assets, the investors are usually concerned with the sensitivity or the duration of the overall portfolio to the changes in the rate of interest. If it is expected that the market rate of interest is going to decline, then it is possible to manage the risk by increasing the duration of the portfolio or vice versa. It is evident that fixed-income assets portfolios are sometimes difficult to trade. Therefore, changing the duration of the portfolio without trading the assets would require the use of futures contracts. These future contracts are less expensive, more liquid and very easily sold in the market as compared to bonds. Thus, for increasing the duration of the portfolio of bonds, it would require buying the futures bond. While, for declining the duration of the bonds, it is needed that the portfolio of bonds is sold. This is evident in the following computations:
Sell bond futures=
num of futures to sell=(yield beta)((〖MD〗_T-〖MD〗_P)/〖MD〗_F )(V_P/(P_f*multiplier))
num of futures to sell=(1.5)((3-8)/2)(47500000/215000)
num of futures to sell=(1.5)(-2.50)(220.93)
num of futures to sell=-828.49
Thus, 828.49 bond futures can be sold to reduce the duration of the portfolio to 3 years.
