INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Hedge Fund Strategies
Final Examination
Name: ___________________
Roll No.: ____________
Instructions:
1. This is a 2-hour written open-book examination; you are allowed use notes or books.
2. You may use a calculator and computer.
3. You are not allowed to use any online resources.
4. Correct answers for each question should be written in the stipulated area.
5. Please submit your Excel file (electronically) also highlighting the answers with yellow
background.
6. Answer questions 1 to 4 and any three from the remaining. (Maximum Marks:50)
__________________
Question 1
(5 Marks)
Consider a convertible bond with one year to maturity, nominal value of $1000, paying one final coupon
of $40 at maturity, with no call and put features. There is no default risk. One bond can be converted into
one share. The current stock price is $900 and, over the next year, the stock price will increase by 20% or go
down by 20% (i.e., the stock price either changes to 1.2 times its previous value or 0.8 times its previous
value). The risk-free rate is 2% per year.
(a)For every convertible bond that you own, how
many shares must you short to hedge your
exposure to the stock?
(b) What is the risk neutral probability of the
share price being $108 one year from now?
(c) A hedge fund buys one convertible bond for
1030 and, immediately after, the market changes
as follows. First, the stock price remains $900,
but the future stock price will now increase by
40% or go down by 40%. Second, the convertible
bond becomes fairly priced. The profit or loss of
the hedge fund is
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 2
(5 Marks)
The following table reports summary statistics for portfolios of currency carry trades implemented during
Jan 1990-Jun. 2012 (N = 270 months). The portfolio composition is determined by sorting currencies based
on their prevailing 1-month LIBOR rate and going long (short) currencies with the highest (lowest) interest
rates. Portfolios are rebalanced monthly, and allocations to individual currencies are spread-weighted (SPR)
or equal-weighted (EQL). Means, volatilities, and Sharpe ratios (SR) are annualized; t-statistics reported in
square brackets. Explain the return and risks of currency carry trades using results from the given table.
Mean
Volatility
Skewness
Kurtosis
Minimum
Maximum
Carry
SR
SPR
0.0521[2.62]
0.0942
-1.04
6.08
-0.1383
0.086
0.0532
0.55
EQL
0.0336[2.39]
0.0667
-0.71
4.6
-0.0836
0.0562
0.0405
0.5
Source: Jurek Crash-Neutral Currency Carry Trades, Journal of Financial Economics, 2014,
Answer:
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 3
(5 Marks)
Using the results in the following tables examine return predictability of commodity futures.
Table 1 shows the annualized return to a strategy of going long the Goldman Sachs Commodity Index (GSCI)
for one month if the previous one-year excess return was positive and going short the GSCI if the previous
one-year excess return was negative.
Table 1 GSCI Momentum Returns (t-statistics in parentheses)
Trailing Annual
Excess Return
Greater than 0
Less than 0
12/1969–
12/1969–
2/1982–
5/2004
12/1982
5/2004
13.47%(2.98)
17.49%(2.12)
11.34%(2.1)
–5.49%(–1.31)
–9.89%(–1.26)
–4.07%(–0.68)
Table 2 provides the results of a trading strategy based on the term structure of individual commodity
futures
Table 2GSCI Term Structure for Trading (July 1992–May 2004)
Portfolio Strategy
Return SD
SR
Long if GSCI backwardated
11.25% 18.71%
0.6
Long if GSCI contangoed
–5.01
17.57
–0.29
Source: Erb and Harvey (2006) The Strategic and Tactical Value of Commodity Futures, Financial Analysts
Journal, 62 (2)
Answer:
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 4
(5 Marks)
Consider a merger arbitrage hedge fund facing the following situation. The risk-free interest rate is 0%.
The objective probabilities of boom, calm, and bust (three possible states of nature) are 1/3 each. The
hedge fund invests in a well-diversified portfolio of merger trades that eliminates all idiosyncratic risk. All
trades will be resolved next time period. The average arbitrage spread is 8%. In case of deal failure, the
expected return is -30%. In case of boom or calm, the failure probability is 4%. In case of bust, the failure
probability is 25%.
(a) What is the payoff of the merger portfolio in
each scenario?
Bust
Calm
Boom
(b) What is the expected return on an unhedged
investment in the merger arbitrage portfolio?
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 5
(10 Marks)
Use the data in the Excel file in the tab called “CPHF” and answer the following questions
a
What monthly Sharpe ratio has hedge fund CPHF
realized before fees?
b What is the maximum drawdown of hedge fund CPHF
before fees (as a percentage of the high water mark)?
c
What is the hedge fund’s univariate market beta using,
respectively, 1-month excess returns (beta1M) and
rolling (overlapping) 3-month excess returns,
computed by summing monthly excess returns
(beta3M) for CPHF (before fees) and Mkt-RF:
d
Based on the hedge fund’s exposure to the 4-factor
model (Mkt-RF, SMB, HML, UMD) using a monthly
regression (before fees),
Mkt-RF
SMB
HML
UMD
e
Each month, the hedge fund first charges a 0.10%
management fees and then a 20% performance fee
without a high water mark (and a zero hurdle rate).
I.e., if the return after management fee is negative
then no performance fee is charged. What is the
Sharpe ratio net of fees?
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 6
(10 Marks)
Consider a market neutral hedge funds invested in the “Betting Against Beta” strategy. The following
assets can be traded
Asset class
Expected annual return E(𝑟𝑡 )
Market β
Risk free
2%
0
Portfolio of low β stocks
6%
0.5
Market portfolio
7%
1.0
Portfolio of high β stocks
8%
1.5
The hedge funds estimate the following excess returns of the low-β and high-β portfolios:
low β
𝑟𝑡
= 𝛼
low β
low β
+ 0.5 𝑟𝑡market + 𝜀𝑡
𝑟𝑡high β = 𝛼 high β + 1.5 𝑟𝑡market + 𝜀𝑡high β
𝑙𝑜𝑤 β
where all 𝑟𝑡 ’s are excess returns, and the error terms 𝜀𝑡
𝑙𝑜𝑤 β
each other, have zero means E(𝜀𝑡
ℎ𝑖𝑔ℎ β
) = 𝐸(𝜀𝑡
ℎ𝑖𝑔ℎ β
and 𝜀𝑡
are independent over time and of
𝑙𝑜𝑤 β
) = 0, and annual volatilities of √var(𝜀𝑡
)=
√var(𝜀𝑡ℎ𝑖𝑔ℎ β ) = 4%. The expected returns of stock portfolios and the risk-free asset are given above.
(a)Let 𝑤𝑟𝑓 , 𝑤𝑙𝑜𝑤 , 𝑤𝑚𝑎𝑟𝑘𝑒𝑡 , and 𝑤ℎ𝑖𝑔ℎ denote the
portfolio weights of the investment in each of the
asset classes. According to its investment mandate,
hedge fund AAA should target a gross leverage of 2.
Suggest two portfolio choices acceptable.
(b) What is 𝛼 low β ?
(c)Hedge fund BBB targets a volatility of 10% (no
target on gross leverage). What is the expected
excess return (i.e., above the risk-free return)?
Choice1:
Choice2:
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 7
(10 Marks)
Use the data on excess returns in the Excel file in the tab called “CTA1” and the following. The trendfollowing managed futures hedge fund CTA1 invests in the listed instrument starting January 1, 1981. Each
month, CTA1 estimates the direction of the trend based on the past 1-month excess return. Each position is
scaled to 10% monthly volatility based on the past 12 months returns.
a) What percentage of the months is the strategy
long Gold?
b) What is the average absolute position size for
Corn?
c) Compute the monthly SR for the trend-following
strategy for each instrument. What is the
average of these Sharpe ratios:
d) Consider the equal-weighted (EW) portfolio of
these risk-controlled trend-following strategies.
What is its SR:
e) Starting on January 1, 1982, another hedge fund
CTA2 uses the following strategy: If the sum of
the past 12 months excess returns on the EW
portfolio from question 28 is positive, then use
this EW strategy. Otherwise, stay out of the
market the next month. The SR is:
f) Starting on January 1, 1982, a third hedge fund
CTA3 uses the following strategy: First, for each
instrument, consider if the sum of the past 12
months excess return on its trend-following
strategy is positive. If so, use the strategy for
this instrument, otherwise put the money in Rf.
Then make an average across instruments. The
SR is:
INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE
Post Graduate Programme in Management
PGPFIN-01 Term V END-TERM EXAMINATION
Question 8
(10 Marks)
Explain the following trading strategies
(a) Selling correlation risk
(b) Swaps spread arbitrage