Unformatted text preview: Question 3
Part (a)
0.04797 <= Depreciation rate on CNY, Nov 2006  Nov 2007
0.0361 <= U.S. 1year interest rate, Nov 2007
0.01187 <= UIPimplied CNY interest rate, if expected depreciation is same as realized
UIP, in the simple additive form, is
i_{cny}  i_{usd} = E_t (log(S_{t+1}/S_t)
If students us either of
(1+ i_{cnyu})/(1+i_{usd} = E_t S_{t+1}/S_t OR i_{cny}  i_{usd} = E_t (S_{t+1}/S_t) 1
That is fine. My answer uses logs.
The upshot of the question is that you expect the policy to remain the same over the next 12 months, so that the expected
depreciation rate on CNY is roughly NEGATIVE 4.7%, the same as it has been over the last 12 months. The UIPimplied CNY interest rate is equal to the USD interest rate plus the expected rate of *depreciation* on CNY. The latter is
roughly about NEGATIVE 4.48%, so the implied CNY rate is NEGATIVE 1.02%.
A range of answers should be given full points here. Any of the above formulations for UIP are fine. So is the answer
"CNY appreciated by around 4.8\%, so if we expect the same over the next 12 months, and if U.S. rates are 3.61%, then
implied CNY rate is 3.614.8 = 1.19%.
Note that the reason for the confusing "appreciation/depreciation" stuff is that, by market convention, the data come as
CNY/USD. Therefore, when we compute the rate of change of the exchange rate as 7.5014/7.87, we are, by definition,
computing the CNY *depreciation rate*. It is reasonable to expect students to be comfortable with this since we've been
doing the similar thing for USD in the class notes all semester long. Part (b)
bid
0.0364 ask
0.0751 <=CNY interest rates 7.5014 Spot CNY/USD
7.1416
7.1416 Expected Spot CNY/USD in 12 months
Spot CNY/USD in 12 months
7.5036 Forward CNY/USD (bid)
1.0000
7.503572
0.3620
0.048258 Pay USD 1.0
Receive CNY
Expected, CNYdenominated, profit per USD of notional
Expected, CNYdenominated, profit per CNY of notional The expected profit on "Pay USD 1.0, Receive CNY" is F_{cny/usd}  E_t S_{cny/usd, t+1}." The forward rate must
involve the CNY bid interest rate, since we are long CNY (ie, lending CNY).
Note that this is roughly the same as the following. The interest rate differential on "borrow USD, lend CNY" is i_{cny} i_{usd} = 3.64  3.61 = .03. So, you get 3 basis points of spread, before the exchange rate effect. The expected
exchange rate effect, from part (a) is around 4.8%. So the total "excess expected spread" is 4.8% + .03% = 4.83%.
This "rate" is in CNY units, since the exchange rate is in CNY units. So it is the expected excess payoff, per CNY in the
forward contract. Since there are (roughly) 7.5014 CNY units in each forward contract with USD notional of 1.0, this
amounts to an expected payoff of .0483 * 7.5014 = CNY 0.362, the same as we got above.
Either answer gets full points. Start
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End
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Frequency D
Name
CH CHINESE YUAN TO US DOLLAR (AVERAGE AMOUNT)
Code
CHXRUSD.
CURRENC CH
########
7.870
########
7.809
1/31/2007
7.790
2/28/2007
7.755
3/30/2007
7.739
4/30/2007
7.725
5/31/2007
7.670
6/29/2007
7.633
7/31/2007
7.581
8/31/2007
7.575
9/28/2007
7.526
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7.501 0.04684 <=exact
0.0458 <=eyeball ...
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 Spring '08
 unknown
 United States dollar, CNY

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