2018 prelim commentary

Investment Management
Easter 2018
Eric Dyke

Limit-
Buy
Order
Stop-
Buy
Order
Stop-
Loss
Order
Limit-
Sell
Order
Action
Price below
the limit
Price above
the limit
Buy
Sell
Condition
Market orders Buy or sell at the best current price
Limit orders specify limits
on the maximum buy or
minimum sell price
Stop loss: Contingent order for someone wishing to
protect a profitable long position, or limit its losses,
if it drops to a given price. It then becomes a market
order; it does not guarantee sale price.
Stop buy order Contingent
order for someone wishing
to protect a profitable
short position, or limit its
losses, if it rises above a
given price. It then
becomes a market order; it
does not guarantee
purchase price
1a. Explain the difference between a stop buy order
and a stop loss order. (7 marks)
Question 1a
Stop buy order definition
3
Stop loss order definition
3
Both are for exiting positions / limiting losses
1

You are given the following option prices on a stock, which is currently trading
at 100. A 1-year call with exercise price 90 is valued at 26 and a 1-year put with
exercise price 90 is valued at 10; and a 1-year call with exercise price 110 is
valued at 18 and a 1-year put with exercise 110 is valued at 13. Demonstrate
whether there are arbitrage opportunities? (9 marks)
Arbitrage free, require PV(X) = S+P-C
Assuming rf = 0% and arbitraging
both sides of put-call parity equation
is incorrect but was worth 2 marks
Present profit on trading future sum of
100 is 93.33-86.36 = 6 .97
X
C+X/(1+r
f
)
S+P
90 116.00 >
110.00
110 128.00 >
113.00
Borrow at low rate and lend at
higher rate
Call
Put
S
X
26 10
100
90
18 13
100
110
Question
1b
Implicit
rf for 90 (Or NPV comparison
) 7.14% (0.933)
3
Implicit
rf for
110 15.79% (0.864)
3
Opportunity for arbitrage?
3
Buy future money (lend) at low price
and sell (borrow) at high price
Future profit on trading present
sum of 100 is 15.79 -7.14 = 8.647
97.69333.0)4675.7(93.33 toScaled 
 = 0.9333
 = 0.8636
 = 7.4675
PV(X)
rf
84.00
7.14%
95.00
15.79%

You are given the following information about a portfolio, denoted A, and the
market portfolio. The risk free rate is 3%.
According to the Treynor-Black model, the optimal mix of the A and market
portfolios for variance-averse investors is given by the formula
In this formula, w* is the weight on portfolio A, αA is Jensen’s alpha of portfolio A,
βA is the beta of portfolio A, rm is the expected return on the market portfolio, rf is
the risk free return, Var(eA) is the idiosyncratic risk of portfolio A, and σm2 is the
variance of the market portfolio. Work out the optimal weight w*. (9 marks)
Portfolio A Market portfolio
Expected return 10% 8%
Variance 12% 9%
Beta 0.8 1
Question
1c
Alpha 3%
3
Idiosyncratic risk
6.24%
3
W* =
0.74 and passive 0.26 9 marks for this
3
))(( fmAfAA rrβr-rα
%3%))5(8.0%3( %10  -
2222 mAAeA
%24.6%)9(64.0%12 
And hold 26% in the market portfolio.
 = 
 = 
 = 0.74
Var(eA) =

5
How does the expectations hypothesis differ from the
segmentation hypothesis as a theory of the term
structure of interest rates?
(7 marks)
Question 2a
Expectations hypothesis
3
Segmentation theory
3
Differences
1