ResponseGroup MembersFamily NameGiven NameStudent ID #
Enter your response here. Alter the size of the box, if required. Please clearly reference any quantitative work doen elsewhere in the workbook.
ReturnsHPRsTSXMSCI USAUnhedgedHedgedDatein C$In US$US$US$1/31/02-0.004362107-0.0141019086-0.00382133680.00022552152/28/02-0.0003742241-0.0195259140.00899257950.0001823673/29/020.03015090030.0372887259-0.00567154880.00018697414/30/02-0.0233730308-0.0648573452-0.01610881280.00025072085/31/020.0004419109-0.007438094-0.02656558580.00043320386/28/02-0.064554355-0.0762089972-0.00464659690.00064136137/31/02-0.0746793699-0.07188819190.04168584390.00071668098/30/020.00221748120.0047604594-0.01533800420.00085842339/30/02-0.0629425065-0.11284149720.01679487180.000948717910/31/020.01212312540.0908375112-0.01305005670.00085739511/29/020.05276650610.06019417550.00070265090.000945384912/31/020.0091397332-0.06038970360.00842589050.00118728461/31/03-0.0054126604-0.0241492126-0.03051019120.00121534372/28/03-0.0002108557-0.0152201879-0.02729172110.0011425963/31/03-0.02974644360.0093123821-0.01265270510.00138273594/30/030.03906347510.0835486759-0.02471192090.00152282545/30/030.04320399060.0536558396-0.04272968070.00179841076/30/030.02054984150.0123944538-0.01059491740.00165295277/31/030.04009081760.01856990190.03643054280.00200919968/29/030.03625653450.0187639068-0.01498313510.00175394999/30/03-0.010009927-0.0115437399-0.02717802690.001456223210/31/030.04841893540.0570827433-0.02326873910.001474674911/28/030.01246813560.0096816398-0.01377034260.001426349512/31/030.0483204470.0519631817-0.00588506810.00148472961/30/040.03753587350.01811704290.02952215130.00140065782/27/040.03243066080.01213346930.00853126880.00121016243/31/04-0.021079013-0.0158823437-0.02049562140.00106577234/30/04-0.0389019781-0.01535360960.04641430470.00098154845/31/040.02254856110.0133019576-0.00774404650.00086529726/30/040.01728198090.0188912968-0.01747764910.00082808157/30/04-0.0092407012-0.0340486171-0.00876375160.0006115988/31/04-0.00809851640.00512022-0.00857787810.00048156519/30/040.03670174950.0109803691-0.0395036430.000402246510/29/040.02436949550.0152926089-0.03618979890.000450397111/30/040.019409650.0411218627-0.0251690920.000508300912/31/040.02642685790.03505374060.00765316850.0003364031/31/05-0.0039804354-0.02475663530.03555481370.00020030882/28/050.05172819810.0208553143-0.009308885803/31/05-0.0037806451-0.0159713656-0.015741946-0.00005694764/29/05-0.0238039383-0.01806766110.0372773484-0.00021490275/31/050.026897340.0326910471-0.0006374756-0.00044623296/30/050.03327525290.0025060683-0.0234023043-0.00052625287/29/050.0531161430.03757395940.0009389288-0.00066949718/31/050.0250403692-0.0092856318-0.0308740161-0.00083200789/30/050.03413355540.0085687404-0.0231461998-0.000866930410/31/05-0.0565044453-0.01640500580.0163277615-0.000844390811/30/050.04417783690.0404071494-0.0093255903-0.000856258712/30/050.04411895650.0005614527-0.0003423046-0.00094133761/31/060.06061280.0272947893-0.0212729 ...
6. 40.1098657618-0.04683076630.00075812111/30/11-
0.0021122077-0.0027416760.0236597030.000694689212/30/11-
0.01699010140.00946706760.00147528890.0007868208
FIN 412 Group Assignment 3
G. Smith Due: December 4 by 5:00 PM
Preliminary commentary: Investing abroad
Consider what happens when an investor makes an investment
outside his or her country of
domicile. As an example, consider a Canadian making an
investment in a US equity index ETF
that trades in the United States. Because the asset trades in the
US, the investor must first buy
US dollars (USD). The investor then takes those US dollars and
purchases the ETF.
Consequently, our investor is exposed to two things that have
uncertain returns, the USD ETF
and the US dollar itself.
Suppose our investor does this, purchasing an ETF at time 0 at
USD price P0. The exchange rate
at the time of purchase was C0, which represents the number of
Canadian dollars (CAD) per US$
at the time of purchase. Thus, the value of the purchase in
7. Canadian dollar terms is P0C0.
Suppose, one period later, we wish to know the holding period
return (HPR) from this
investment. At the end of period 1 the US dollar price of the
ETF is P1 and the exchange rate is
C1, meaning the CAD value of the investment is now P1C1.
Consequently, the HPR over the
period is given by: 1 1
1
0 0
1
PC
HPR
P C
You can see clearly from the above that the Canadian investor’s
return is a function of the USD
return on the investment (P1/P0, which is (1+HPR) for the ETF
in US) and percentage change in
the exchange rate (C1/C0, which is (1+HPR) to a Canadian from
holding one USD).
A quick numerical example follows. Suppose our investor buys
a share of the ETF at time 0 and
8. is computing his HPR at the end of period 1. For simplicity,
assume no dividend is paid. Prices
and exchange rates are as follows:
Time USD Price
per share
CAD/USD
0 $10 1.03
1 $11 1.01
Two relevant things happened over the period. The price of the
ETF went up by 10% and the
CAD appreciated relative to USD (equivalently, the USD
depreciated relative to CAD). The HPR
experienced by a US investor is 10%, but our Canadian investor
is less fortunate. The Canadian’s
ian’s
return is lower than that received by a US investor as the USD
became less valuable over the
holding period. One can easily see that if the currency had
moved in the opposite direction to
that of the example, our Canadian investor would have received
a higher return than a US
investor holding the same ETF.
9. FIN 412 Group Assignment 3 Due: Dec 4 by 5:00 PM
2
Currency returns can be quite volatile. As the numbers above
show, currency movements
impact returns experienced on foreign investments. Few
investors make foreign equity
investments because they want the currency exposure. There are
much simpler and more
direct ways to get the currency exposure, should that exposure
be sought. Typically, foreign
investments are sought because they are thought to be able to
improve a portfolio by offering
better returns or enhanced diversification. Thus, the potential
currency impact can be troubling
to investors
Fortunately, the advent of derivative markets has made it
possible for investors to hedge the
currency risk inherent in an international investment. The
example above demonstrates a
straightforward, unhedged investment by a Canadian in a US
equity. Our investor could have
10. proceeded differently. To hedge the currency risk in this
investment, the investor could have
done the following at initiation of the investment:
rate at which you would sell
the USD at a future date.
This has eliminated the currency risk related to this investment.
Note that there would still be
some currency impact, as the forward price at which one
contract to sell the USD will, in
general, be different from the spot rate.
1
However, this impact would be certain as we would
have contracted a price at which to sell the USD at the end of
the period.
The point of all this is to say that currency effects can be
significant, but that we are able to
hedge these effects by using derivative positions. We can hedge
the currency risk. The
important question is if we should do so.
The Question
11. You work as an analyst at a Canadian institutional investment
manager. Your firm is about to
begin a passive investment program in the US equity market,
wherein the firm will replicate the
MSCI USA index, a broad market capitalization-weighted US
equity index. This passive portfolio
will be make up 50% of your firm’s equity portfolio, with the
other 50% being a S&P/TSX
Composite Canadian Index passive replication fund.
Your firm’s investment committee is grappling with the
question of whether or not the currency
exposure inherent in the US investment should be hedged. The
committee chairperson makes
the following statement:
1
Pricing and general structure of currency forward contracts is
beyond the scope of this course, but is touched on in the
textbook and is covered extensively in other courses (e.g. FIN
413).
FIN 412 Group Assignment 3 Due: Dec 4 by 5:00 PM
3
12. “The whole purpose of our investment in US equities in the first
place is to improve the risk
characteristics of our overall portfolio. It is a market that is not
perfectly correlated to our
Canadian equity assets, so our portfolio will be improved in
terms of expected return to risk by
making this change. But I have no opinion about the direction
of the US dollar relative to the
Canadian dollar and I never will. It is just too unpredictable.
Over time, returns to holding
currency are effectively zero. But it’s the volatility that comes
from the currency that concerns
me. I want equity exposure from the US market. The currency
component is an unsought risk
factor, so I think we should hedge the currency component. Why
take a risk that we are not
seeking when we can easily eliminate it? It seems pretty
obvious that we should hedge the
currency exposure.”
Given the committee chair’s stated purpose of the US
investment and his expectation that
currency returns average zero over time, do you agree with his
conclusion that the currency
13. exposure inherent in the US Equity investment should be
hedged? Explain your answer.
To assist you in your analysis, the companion spreadsheet
contains 10 years of monthly returns
data on the S&P/TSX Composite Index (in CAD terms), MSCI
USA (in USD terms), unhedged
returns to a Canadian from holding USD, and returns to a
Canadian from holding one-month
forward hedged USD positions. We know that historical data
can give us a good idea of
variances and correlations, but is less helpful in giving us an
idea of future expected return.
Thus, in your analysis, assume that the expected return on
currency is zero and that the
expected return on both equity indexes are equal, but that the
volatility and correlation
structure inherent in the provided data is representative of what
will hold in the future.
