Hi, can anyone please what is the meaning of this phrase: “Forward exchange rate is an unbiased estimator/predictor of future spot rate”.
Specifially, I am try to understand what does ‘unbiased’ mean in the phrase above.
When an estimator is described as unbiased, it means that its expected value is equal to the value it is estimating. You should recall this from Level I: three desirable characteristics in an estimator are that it is:
- Unbiased – its expected value equals the value it is trying to estimate
- Efficient – it has the lowest sample variance of all unbiased estimators
- Consistent – its sample variance decreases as the sample size increases
So, for example, a sample mean is an unbiased estimator of the population mean because:
E(X-bar) = μ
If we use the sample size n in the denominator for the sample variance, then its expected value is not the population variance; however, if we use (n – 1) in the denominator, then its expected value is the population variance. (Note that the proper name for the sample variance using (n – 1) in the denominator is the bias-adjusted sample variance; it removes the bias.)
Finally, the expected value of the forward rate is the future spot rate; hence, the forward rate is an unbiased estimator of the future spot rate.
Don’t get too caught up with the word I’d think.
To me I see it as in theory, the forward exchange rate, given all the known and definite factors (no uncertainty/unknowns), would implicitly be the future spot rate.
however in practice, it isn’t so simple and surrounding factors do influence the value of future spot rate.
thanks s2000magician, nicely explained.
helloatlas, yea i tend to get bogged down on some minor things but they bug me a lot so had to understand them.
yea thats what i thought as well, if forward rates can predict future spot rates then there shouldnt be volatility in the fx market, but many many factors influence exchange rates.
My pleasure.
I agree with helloatlas.
The idea behind the “unbiased” predictor is explained by 2 main factors: arbitrage and unpredictability.
Exchange rates are unpredictable, so no model can predict with certainty the short-term movement of exchange rates. However, with the information we have today, we can arrange contracts of future exchange rates. Those forward rates need to foresee the impossibility of arbitrage, if not, you are feeding others’ wealth for free. In conclusion, to prevent arbitrage, we need to correctly calculate the forward exchange rate in function of the interest rates related to the currencies we are trading. This is the most usefull predictor we have.
Note that forward exchange rates have failed many many times in predicting future spot exchange rates, at least the short-term ones.
A lso note that the forward exchange rate equation is known as the covered interest rate parity.
I also wouldn’t call it this a “small point”. The idea of unbiased estimation, as S2000 has pointed out, is a statistical concept. I would think it’s fair game in any part of the QM section.
I think that you’re confusing forward rates and future spot rates. Forward rates are constrained by arbitrage; future spot rates are not.
When you enter into a forward contract on an exchange rate, you no longer care what the spot rate will be: you have locked in a rate with the forward contract.
I wasn’t clear enough with the phrase “we can arrange contracts of future exchange rates”. I tried to mean that when we accord a forward rate we are subject to that rate to be exercised in the future, despite what the spot rate will be. Please note that I didn’t mention “spot rate” in my sentence, so I think I am not confused about this.