I’m confused about the difference between something being a biased predictor of future spot rates vs. being an unbiased predictor.
We see this in at least two areas of the curriculum: 1) Economics (Biased vs. unbiased predictor of future spot rates), and; 2) Derivatives (are Futures prices biased or unbiased predictors of future spot rates or prices).
Can someone please simplify for me? Thanks.
An unbiased predictor of something has an expected value that is equal to the value it’s trying to predict; a biased predictor has an expected value that is not equal to the value it’s trying to predict.
For example, a sample mean is an unbiased predictor of the population mean: E(X-bar) = μX. A sample standard deviation (calculated according to CFA Institute) is an unbiased predictor of the population standard deviation: E(sX) = σX. However, if we calculated the sample standard deviation by dividing by n instead of dividing by n – 1, then it would be a biased estimator: its expected value would not be the standard deviation of the population (it would . . . no surprise . . . be too small by a factor of (n – 1) / n). By the way, the proper name for the sample standard deviation (calculated according to CFA Institute) is the _ bias-adjusted _ sample standard deviation: a sample standard deviation adjusted to remove the bias, (the adjustment being to divide by n – 1 instead of by n).
Anytime there’s a question I’m uncertain of s2000magician has already answered it. Thanks, sir.
My pleasure.