So I am reading a very nice book, "
Hedgehogging" which tells stories about hedge fund and the people.
As I am from a statistics background, I am automatically sensitive to numbers (with uncertainty) and probability and the combination of the two. In Chapter 8, I am impressed by an example that the author cites from "
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets".
The example says:
You are an excellent investor, and are able to gain additional 15% return above US bond. The variability (standard deviation) of your return in a year is 10%. (Assuming your return rate follows a normal distribution ), then you have about 93% chance to gain more then the US bond in a year.
Then the author cites a table from that book which illustrate the relationship between the probability that you gain more than US bond and the time frame you are checking your return. However, the results in table from the original book are simulation based. Actually, we can calculate the exact number for the table. So I automatically cannot help calculating it and update the table as follows --
If you compare results in this table with the original table, you will see very tiny difference.
Here is formula to calculate the probability that you will gain more than US bond, given that you gain 15% more than US bond and the standard deviation of your return in a year is 10%.
Let X_t be your return in a time span T. Let N be number of period of time span T to be a year. For example, N=3 means time span T is 4 month, which is one season; N=365 means time span T is a day. Assuming X_t also follows a normal distribution and X_t's are independent of each other; therefore, X_t ~ N(mu, sigma/sqrt(N)), where mu is 15% and sigma is 10%. Thus, the probability you gain more than US bond,
P(X_t>0 ) = P_norm(mu/(sigma*sqrt(N)))
P_norm is cumulative probability function of standard normal distribution.
The follows is a simple R code to calculate the above:
u=0.15 # on average you earn 15% more than US bond per year
sig = 0.1 #variability of your annual return
prob_noloss <- function(u, sig, T) pnorm(u/(sig*sqrt(T)))
#probability you gain more than US bond per year
prob_noloss(u,sig,T=1)
#probability you gain more than US bond per season
prob_noloss(u,sig,T=3)
#probability you gain more than US bond per month
prob_noloss(u,sig,T=12)
#probability you gain more than US bond per day
prob_noloss(u,sig,T=365)
#probability you gain more than US bond in per hour
prob_noloss(u,sig,T=365*24)
#probability you gain more than US bond in per minute
prob_noloss(u,sig,T=365*24*60)
This example may looks simple and have strong assumption in the calculation. But the way that the authors (from both books) are valuable.
As discussed in the book (the Hedgehogging book), now suppose you are a fund manager and your, when clients of your look at annual return, they will have a high probability of feeling happy and thus have strong confidence holding putting money in your fund. But, if they are able to look at your return everyday, their happiness will decrease, thus some (or many) of them may pull their money out of your fund, which then will make you nervous, worried, maybe angry, and may make you make irrational decisions.
Actually, this is chain effect not only just apply to fund managers. To individual investors, it is the same because we are managers of "our fund". That is why I feel quite impressed when the author mentioned this first from citation of simple statistics example and come to a common phenomenon in the market -- falling into the trap of randomness.
However, it seems the author (of book: fooled by randomness) would not forbid managers or investors from looking at their daily return, but instead he recommends that we should just need to know our performance in this trading day, but keep calm when making decisions, not driven by our mood, which I feel is a true statement but just too general to follow.
I am still in progress of reading this nice "Hedgehogging" book. Hope I can learn more from it and will keep posted when new interesting thing is found.