Question

The following table shows the US$/C$ spot rate and forward rates as of January 11, 2019.

USS/CS rate 0.7555 Spot 1 month 3 months 6 months 1 vear Source: http://fx.sauder.ubc.ca 0.7559 0.7569 0.7583 0.7608

(a)

Covert the above exchange rates into the direct quotes.

(b)

Does the forward rate structure imply that the Canadian dollar will depreciate or appreciate against the US dollar over the next

year?

c)What is the implied annual rate of appreciation/depreciation of the Canadian dollar against the US dollar over the next

three months, over the next six months, and over the next year?

d)Now, say the two-year forward rate is US$0.7644/C$. What is the implied annual rate of appreciation/depreciation of the

Canadian dollar against the US dollar over the next two years?

e)What is the implied annualized rate of appreciation/depreciation of the Canadian dollar against the US dollar

between year 1 and year 2?

Note: Assume there are 30 days in a month.

Answer 1

(a) Indirect quote: US$ / C$ = 0.7555 i.e. 1 C$ = US$ 0.7555

Direct quote: 1 US$ = (1 / 0.7555) C$

1 US$ = 1.3236 C$

C$ / US$ = 1.3236

Concept: Direct Quote is the value of foreign currency (which is C$ in the given question) for 1 unit of domestic currency (which is US$ in the given question)

(b) As per the forward rate structure given in the question, the Canadian dollar will appreciate against the US dollar over the next year.

Explanation: Spot rate of 1 C$ is US$ 0.7555 which after one year (forward rate) appreciates to US $0.7608. (You have to pay more US$ to purchase 1 C$ which implies that C$ has become costlier (appreciated).

(c) Implied rate of annual appreciation of C$ Over next 3 months Spor rate Forward rate (3 months) - 0.7569 Annual appreciation 0.7555 Forward Rate - Spot Rate 360 X 100 Spot Rate 0.7569 0.7555 0.7555 360 X 100 90 074% Over next 6 months Spor rate Forward rate (6 months) Annual appreciation 0.7555 0.7583 - Forward Rate - Spot Rate 360 X 100 Spot Rate 0.7583- 0.7555 0.7555 360 X 100 180 074% Over next 1 vear Spor rate Forward rate (1 year)0.7608 Annual appreciation 0.7555 Forward Rate - Spot Rate 360 X 100 Spot Rate 0.7608 -0.7555 360 X 100 0.7555 360 0.70%

(d) Implied rate of annual appreciation of C$

Over next 2 years Spor rate Forward rate (1year)0.7644 0.7555 360X Forward Rate - Spot Rate Spot Rate Annual appreciation _ X 100 360X 720 o.rix (0.7644- 0.7555) 0.7555 X 100 0.59%

(e) Depreciation of C$ between year 1 and year 2

(1 + Appreciation in Year 1) * (1 - Depreciation in Year 2) = (1 + Appreciation over 2 years)

1.0070 * (1 - Depreciation in Year 2) = 1.0059

(1 - Depreciation in Year 2) = 0.9989

Depreciation in Year 2 = 0.0011

Depreciation in Year 2 = 0.11%