page 582 portfolio No.18

the answer of text page 582 portfolio management No.18 says perfect timing performs better than T-bill. but i don’t agree, the sharp ration of t-bill is higher than perfect timing 0.21/0.17>2.58/3.82, is answer wrong? the answer also mentions standard deviation is a missleading indicator, i don’t get it, if no standard deviation, which measure will measure risk? does perfect timing means fatcor titlt? factor tilt and stock selection are two ways of super fund meausrement

any expert here? thanks

The reason the standard deviation is missleading in a perfect market timing scenario is as follows. The risk free rate is assumed to be a guaranteed constant rate, say 5%. We assume this will never go up or down, but stays the same at 5% for the duration. Without any movement we have 0 Std Dev. The perfect timing portfolio will have a standard deviation greater than 0 and here’s why. In perfect timing you are either going to be in risk free or risky whichever performs better, however when you are in the risky portfolio while you know you will outperform you do not know by how much, ie lower bound is 5% but upper bound is some number greater than 5% which allows you to calculate a std dev because the return will not be a constant throughout. This is why you cant compare using Std Dev because if you strictly look at it (which is the denom in sharpe) you might say that this portfolio is riskier than all risk free. However it is completely upside risk (no downside) which is the kind of risk we all want in portfolios. Perfect timing means asset selection not factor tilt.

if Perfect timing means asset selection not factor tilt, can you give a example of factor tilt? you mean perfect timing lower bound is risk free and upper bound more than 5%, I don’t agree, buying stock, return can be negative, so how can you say lower bound is risk free? what’s the measure to compare risk free asset and risky asset since both standard deviation and sharp both can not be used?

Factor tilt comes when a PM decides to overweight/underweight exposure to a given factor based on their belief of future movements. (i.e. market consensus for GDP might be an increase of 3%, but the PM might forecast 4% and choose to overweight/tilt the portfolfio heavier than the benchmark in cyclicals) you are correct in your second point in a real world example, but “perfect timing” means that you always invest in risk free or risky whichever outperforms. In the perfect timing model if stocks are down you would not be in them you would be in risk free which is why it is you lower bound. Obviously that is not indicative of the real world but that is why in perfect timing you cant use std dev or sharpe, but when the PM is not a perfect market timer (i.e. they underperform risk free at times) you would definately look at std dev and sharpe.