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21 Aug 2018

Q1. Suppose you are managing a stock portfolio that is currently valued at $2,000,000. You expect the stock market will be bullish in the next 6 months. But you are also aware of a small chance of market crash and you want to insure that your portfolio value will be at least $1,800,000 in 6 months even in a market crash. In other words, you don’t want to suffer more than 10% loss in the next 6 months. Assume your stock portfolio has a beta of 1.5, the current S&P 500 level is 2,000 and the risk-free rate is 1% per annum.

How would you hedge against your portfolio value dropping below $1.8M in 6 months? Be specific with your strategy. If you are using options, specify what the underlying asset is, the strike price, time to expiration. whether it’s a call or a put and how many units to buy or short.

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Nestor Rutherford
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22 Aug 2018

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Q1. Suppose you are managing a stock portfolio that is currently valued at $2,000,000. You expect the stock market will be bullish in the next 3 months. But you are also aware of a small chance of market crash and you want to insure that your portfolio value will be at least $1,700,000 in 3 months even in a market crash. In other words, you don’t want to suffer more than 15% loss in the next 3 months. Assume your stock portfolio has a beta of 1.4, the current S&P 500 level is 2,000 and the risk-free rate is 3% per annum.

How would you hedge against your portfolio value dropping below $1.7M in 3 months? Be specific with your strategy. If you are using options, specify what the underlying asset is, the strike price, time to expiration. whether it’s a call or a put and how many units to buy or short.

(please show all work)

In the most recent Berkshire Hathaway's annual meeting in Omaha, NE, Warren Buffett said he shed a third of his holdings in IBM due to the highly competitive environment IBM is facing. Shortly after, "Mad Money" Jim Cramer expressed his still bullish outlook for the company by pointing out some possible transformational acquisitions IBM could make for new growth opportunities. Nevertheless, the two ideas represent the mainstream now. Suppose you are not sure about the direction of the stock price movement but believe the stock price of IBM will be more volatile than usual in the next three months, you want to bet on the volatility. You are looking at a call option on IBM with strike price of $155 selling at $3.75 and a put option with strike price of $155 selling at $4.84 (real time market data on May 7, 2017). Both options will expire on Jul. 21, 2017. What option trading strategy you can employ based on the above two options so you could exploit the possible highly volatile IBM stock price movement in the next three months? Plot the trading strategy profit diagram and point out in what price range your trading strategy will see a profit.

Derivative

Vanguard High Yield Corporate Fund
Materials
• Website information (23/05/2016)
https://personal.vanguard.com/us/funds/snapshot?FundId=0029&FundIntExt=INT
• Summary Prospectus (27/05/2015)
• Prospectus (27/05/2015)
Anakin’s Job
In May 2016, Anakin leaves his job in Hollywood and returned to the finance industry. It is his
first love after all and the industry appears to be picking up again after the credit crunch of
2007-2008. He applies to be the risk analyst to the fund manager of the Vanguard High Yield
Corporate Fund as his quantitative training positions him well for a job that requires ever more
numerical and computational skills over the years. His solid background in applied analytics
in business management and humble demeanour help him clinch the post without much
difficulty.
The Vanguard Group is an American investment company that has approximately USD 3
trillion in asset-under-management. It is founded in 1975 by John Bogle who created the first
index fund (tied to the S&P 500 index) in the process. After an initial lull, the index grew
rapidly along with the bull market of the 1980s. The Group has since added various financial
services and products to its core business, particularly the ETFs.
Anakin is tasked by the fund manager to become thoroughly familiar with the structure of the
fund as is documented by files provided under “Materials”. After that, he is to assess the
exposure of the High Yield Corporate Fund to risks in the market. He seeks the opinion of
Darth who is a veteran market analyst with the Vanguard Guard group for over 20 years.
Outlook
Darth has this to say about the economy and fixed income market:
" The US economy is improving steadily. It will not be long before the Fed decides to raise
interest rates. Once the Fed restarts the regime of rising rates, it will about 2 years for the yield
curve to rise by 100 basis points.
Consequently, in the more stringent economic environment, companies of lower credit
qualities, namely those of Caa and below, are expected to have their credit standing further
eroded. There is a 25% chance that a Caa-rated issuer may go into default and another 25%
chance that it may be downgraded to C.
The Greek debt problem, though much stabilized than before, is still a matter of grave concern
for the Eurozone. Expect the euro to depreciate against the dollar over the course of the next 6
months. A fall of 500 pips will not be a surprise. "
Assume Anakins’ role and answer the following questions. Questions 1 and 2 concern the
Financial Environment. The Environment at large provides the context and sets the constraints
within which financial decisions are weighed and taken. Questions 3 and 4 pertain to the task
that Anakin needs to complete.

Question 4
The fund is affected by changes in the financial markets. When interest rates rise, the value of
the portfolio falls. Occurrences that are flagged by the rating agency to be credit events can
result in the downgrading of credit rating of bond issuers. Bonds that denominated in foreign
currency are affected by fluctuations in the foreign exchange market.
(a) Analyse generally the need for hedging the various market risks for the fund.

Take into account Darth’s outlook. Address some of these risk concerns by answering the
following question:
(b) Suppose that in the coming 2 years, the prevailing interest rates are expected to go up
by 100 basis points and you are concerned. Show how you could hedge away the
interest rate risk by using an interest rate swap, assuming that the fund by may
represented by a single 5-year par bond on the $18.4 billion net assets with semi-annual
5% coupon payments starting from the current date.
In your explanation, you may assume a scenario in which a flat yield curve increases
uniformly across all terms by 25 basis points per half-a-year.
(c) Credit default swaps may be used to ameliorate credit risk. Appraise the use of such
option-like derivative instruments in managing the risk of the portfolio by explaining
how such instruments function.

https://institutional.vanguard.com/VGApp/iip/site/institutional/investments/productoverview?fundId=0029

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