156 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY
4.6.2 Common Pitfalls in Computing Effective Returns
To conclude this Appendix we describe the most common mistakes when computing
effective returns. The first is forgetting to de-annualize the return. Always convert
the bank’s quoted interest rate into the effective return over the period (T−t).And
use the correct formula:
Example 4.26
LetT−t= 3/4 years. What are the effective rates of return when a banker quotes a 4
percentp.a.rate, to be understood as, alternatively, (1) simple interest, (2) standard
compound interest, (3) interest compounded quarterly, (4) interest compounded
monthly, (5) interest compounded daily, (6) interest compounded a million times a
year, (7) interest compounded continuously, and (7) bankers’ discount rate?
convention formula result (1+r)
simple 1 + 3/ 4 × 0. 04 1.030000000
compound,m= 1 (1 + 0.04)^3 /^4 1.029852445
compound,m= 4 (1 + 0. 04 /4)^4 ∗^3 /4) 1.030301000
compound,m= 12 (1 + 0. 04 /12)^12 ∗^3 /^4 1.030403127
compound,m= 360 (1 + 0. 04 /360)^360 ∗^3 /^4 1.030452817
compound,m= 1, 000 , 000 (1 + 0. 04 / 106 )^10(^6) ∗ 3 / 4
1.030454533
continuous compounding e^0.^04 ∗^3 /^4 1.030454533
banker’s discount 1 /(1− 3 / 4 ∗ 0 .04) 1.030927835
Second, it is important to remember that there is an interest rate (or a discount
rate) for every maturity, (T−t). For instance, if you make a twelve-month deposit,
thep.a. rate offered is likely to differ from thep.a. rate on a six-month deposit.
Students sometimes forget this, because basic finance courses occasionally assume,
for expository purposes, that thep.a. compound interest rate is the same for all
maturities. Thus, there is a second pitfall to be avoided—using the wrong rate for
a given maturity.
The third pitfall is confusing an interest rate with an internal rate of return
on a complex investment. Recall that the return is the simple percentage difference
between the maturity value and the initial value. This assumes that there is only one
future cash flow. But many investments and loans carry numerous future cash flows,
like quarterly interest payments and gradual amortisations of the principal. We
shall discuss interest rates on multiple-payment instruments in the next appendix.
For now, simply remember that the interest rate on, say, a five-year loan with
annual interest payments should not be confused with the interest rate on a five-
year instrument with no intermediate interest payments (zero-coupon bond).
Example 4.27
If a newspaper says the 10-year bond rate is 6%, this means that a bond with an
annual coupon of 6% can be issued at par. That is, the 6 % is a “yield at par” on