Sample Quiz Flashcards
Trading 1 of 3
List and explain two (2) differences between a margin trading strategy and a short-selling strategy.
(Worth 1 mark)
For a margin trading strategy, the investor borrows money from broker to purchase securities. For the short-selling strategy, the investor borrows the securities from someone (rather than borrowing money as per the margin trading strategy).
For a margin trading strategy, the investor can make a profit when the price of share increases and a profit can be released through the sale. When price of share decreases, a loss may incur if sold and may trigger a margin call by the broker if the share price falls below an agreed maintenance margin and the investor would need to add more cash to cover the costs or buy shares to replace the ones borrowed.
For the short-selling strategy, the investor can make a profit (at sale) by betting the share price would fall (rather than making a profit when the share price rises as per the margin trading strategy). For this strategy, a margin call may be made by the broker if the share price INCREASES above an agreed maintenance margin.
Trading 2 of 3
Beach Energy Limited is currently trading at $2.49 on the ASX. Roosters Equity Fund short sells 2,500 shares in Beach Energy Limited through their broker. The initial margin requirement is 55% and the maintenance margin is set at 30%.
Calculate the initial margin deposit that Roosters Equity Fund must deposit in their margin account with their broker and how much the price of Beach Energy Limited share price will need to change by before they receive a margin call.
(Worth 2 marks)
of Shares = 2500
Initial Margin Deposit
= Initial Margin (%) x Stock Price ($) x # of Shares
If:
Initial Margin = 0.55
Stock Price = 2.49
Number of Shares = 2500
Initial Margin Deposit =0.552.492500
=$3423.75
Therefore, Roosters Equity Fund must deposit $3423.75 into margin account with their broker.
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How Far Stock Price Needs to Increase before Margin Call?
(Investor Makes Short Sale)
If:
Initial Margin = 0.55
Initial Stock Price = 2.49
Maintenance Margin = 0.30
New share price
= (Initial Share Price x (1+Initial Margin)) / (1+Maintenance Margin)
=(2.49*(1+0.55))/(1+0.3)
= 2.9688
Change in share price
= new price - initial price
= 2.9688-2.49
= 0.4788
Therefore, share price must increase by $0.48 before receiving margin call.
Trading 3 of 3
Roosters Equity Fund is interested in profiting from arbitrage trading.
Describe why and how Roosters Equity Fund will use the alphas and betas of the shares in two companies to construct an arbitrage portfolio that has zero initial investment, zero systematic risk and a positive return.
(worth 2 marks)
An arbitrage opportunity occurs when two or more securities prices allow the investors to construct a net zero investment portfolio that will yield a sure and positive return.
The presence of an arbitrage opportunity can be exploited when securities are mispriced in the market and financed by short selling an overpriced asset (or negative alpha). This means zero initial investment. Notably, arbitrage trading can take place when the investor buys an underpriced security when alpha is positive (i.e. alpha is more than and not equal to 0). Further, the investor can purchase two securities when the sum of the alpha values for each security is positive.
Further, a factor mimicking portfolio can be created to be used in the arbitrage portfolio strategy. which mimics the behaviour of a risk factor such as systematic risk of portfolio “P”. The investor could look at company/ies that is very affected by factor and put in that in a portfolio “q” where:
Beta_pk = amount of each risk in portfolio.
E(f_k)-r_f = price of each risk (return premium for bearing 1 unit of risk)
E(r_p) = r_f + beta_pk (E(r_k) – r_f)) = expected return of portfolio
Preferences 1 of 3
The expected return on a diversified risky asset portfolio, Sunrise Fund, is 15.25% while the variance of its returns is 16%. The return on the risk free asset is 4%. Roosters Trust has $100 million to invest and decides to invest $70 million in the Sunrise Fund and the rest in the risk-free asset.
Calculate the expected return and standard deviation on this portfolio. (worth 1 mark)
Describe where Sunrise Fund and the portfolio created by Roosters Trust will lie on the capital allocation line. (worth 1 mark)
Portfolio Expected return:
=(0.70.1525)+(0.30.04)
=0.1188
= 11.88%
In dollars:
= 11.88% * $100,000,000
= $11,875,000
Portfolio expected deviation:
=0.7*(sqrt(16)/100)
=0.028
= 2.8%
In dollars,
= 2.8% * $100,000,000
= $2,800,000
Location of Sunrise Fund and Portfolio created by Roosters Trust on CAL:
Preferences 2 of 3
Roosters Trust has a risk aversion factor of A=2.
Use this information and the information from the previous question to calculate the optimal weights that Roosters Trust should hold in Sunrise Fund and the risk-free asset and the expected return and standard deviation on this portfolio. (worth 1 mark). (worth 1 mark)
Describe where the optimal portfolio will lie on the capital allocation line relative to Sunrise Fund. (worth 1 mark)
Weight
Preferences 3 of 3
Explain how the optimal weight in the Sunrise fund would change if the risk aversion factor of Roosters Trust increases.
(worth 1 mark)
The optimal weight on the risky asset portfolio (w_p) in the Sunrise fund can be calculated from the expected return equation and the utility function.
w_p = (E(r_p)-r_f) / [A_i*(𝜎_𝑝^2)]
The optimal weight (w_p*) decreases as the level of risk aversion, A_i, increases.
Asset Pricing 1 of 3
Roosters Pension estimates that the excess returns for Souths Limited have an alpha of -1.5% and beta of 1.25, while the excess returns for Tigers Limited have an alpha of 3% and beta of 0.7. Are the shares in Souths Limited and Tigers Limited mispriced? Explain you answer.
(worth 2 marks)
Asset Pricing 2 of 3
Explain two (2) reasons why the SIM is more popular than the CAPM.
(worth 2 marks)
Two reasons by SIM is more popular than CAPM:
- CAPM is a theoretical model and relies on theoretical market portfolio that include all assets and consider direct relationship between each asset in portfolio. However not all assets are traded and it may also be unfeasible to estimate variances and covariances for a large number of assets (n(n-1)). The SIM is a statistical model that compares each asset to a proxy/index (similar to a hub and spoke model) and is less time consuming to model the asset returns.
- In an expected return-beta diagram, the beta of the SIM can show how sensitive the stock return is to market fluctuations; whereas the CAPM is not able to do this and can only show how much of a return premium to expect.
Asset Pricing 3 of 3
Describe how factor mimicking portfolios are used in arbitrage portfolio theory. In your answer you will need to explain what a factor mimicking portfolio.
(worth 1 mark)
Factor mimicking portfolio (FMP):
- pure measures of exposure to each risk factor.
- Mimics behaviour of a risk factor such as systematic risk of portfolio P. Look at company/ies that is very affected by factor and put in portfolio (i.e. macroeconomic)
FMP is used in arbitrage portfolio theory when:
- Investors want net investment to be zero and proceeds to be riskless.
- If αP were positive, investors would pursue this strategy (which is riskless and requires zero net investment) at an infinitely large scale and make an infinitely large profit.
- If αP were negative, investors would do the reverse, selling portfolio P and buying the mimicking portfolio, again clearing a risk-free profit.
- These large-scale investments would continue indefinitely until alpha was driven to zero.
