25 April 2011
Future value 6 months from now is a product of future value 6 months from now and 6 months future value from after 6 months (1+.005*6/12) = (1+.045*3/12) * (1+ r*3/12)
This was the formula used to solve forex questionin SFM May 2010 . Question was to calculate 3 months forward rate at 3 months forward Can anybody help me how this formula was derived Is this derived from Fisher International Effect 1+ Nominal rate = (1+ real rate) (1 + inflation rate)
26 April 2011
No it is not derived from Fischer’s formula. Its derived on “no arbitrage” principle. Here is an example:
Suppose one year interest rate is 6%; the interest rate for six months is 5.5%; what is the expected six month rate for the period starting six months from today? Suppose it is r. This r must satisfy the equation (all rates are on per annum basis): (1+.055/2)(1+r/2) = (1.06) This gives the value of r = 6.326%. If we were to expect that the six month rate for the half year starting six months from today should be more than this, then we will borrow (say 100) for one year and lend it for half year and after six months we will have 105.5. We will lend it again for half year at our expected rate (say 6.5%) and end up with 102.75*(1+0.065/2) = 106.09 of this I will give 106 to my creditor who had loaned me 100 for a year and pocket .09!!. This is called money –machine, an arrangement that gives us money without accepting risks. Since we are talking about money market rates, the chances of default are minimal (already taken into account in rates). Presence of sharp arbitrageurs in the market ensures that any such anomaly is quickly exploited till it ceases to exist. If many people (i.e. market) expect the six month rate after six months from today to be 6.55% they will start borrowing for one year and lending for six months thereby increasing one year rate (increased demand for one year money) and decreasing six months rate (increased supply of six months money) till a new equilibrium is reached.
Fischer used the same “no arbitrage” principle in deriving his equation – investors want real return and expect inflation and thus work out nominal interest rate to be charged.
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