Thoughts On Backtesting

So I have a few methodological thoughts on backtesting strategies. The lack of sound methods in studies is problematic in my opinion. If anyone has some insight into this I'd appreciate it.

I'm going to lay out what I consider three common problems in empirical research into backtesting investing strategies. Not all studies suffer from all three problems but I think a lot do. And I think attempting to address these is a good start.

Arithmetic and Geometric Returns

Many times when expressing returns, the arithmetic returns are used instead of geometric returns. This is actually quite problematic. But there are ways of actually relating the two returns which I'll share today.

A Unique Solution to the Monty Hall Problem

The Monty Hall Problem is a counterintuitive result in statistics. The problem goes something like this.

Sketch of the Monty Hall Problem

Suppose there are three doors: A, B and C. Behind one of the doors is a big prize (a car, a huge pile of cash). Behind the other two doors are just some goats.

Now you make a selection of a door but the game is not over with yet. Suppose you pick door letter A. Now the game is not over with yet at this time. The host actually reveals one of the remaining doors, say door letter C, to have a goat.

Now the host gives you the option: stick with door A or switch to door B.

Thoughts on the Sharpe Ratio

So this is going to be just a few musings on the Sharpe Ratio. But before that, I want to do a comparison to a technique I utilized because it has similiarities to the Sharpe Ratio. This is also somewhat related to Cullen Roche's question and my response here.

In my blog post, Are Bond Yield Spreads Adequate?, and the subsequent follow-up, Junk Bonds: A Closer Look, I developed a simple model to analyze spreads to see if they were adequate. Today I'll give a more "intuitive" explanation of that model.

Some Thoughts on Risk/Return Tradeoff and EMH

So this is partly a response to a question asked by Cullen Roche on Twitter:

@dvegadtime @financequant Q: What's your preferred measure of risk adjusted return? Sharpe, SDR Sharpe or Sortino? Thanks.
— Cullen Roche (@cullenroche) October 19, 2013

Is the Stock Market a Ponzi Scheme?

Today I want to explore the question on whether or not the Stock Market is a Ponzi scheme. The reason why is that I think many people view it as such but may not even realize it. So the big question here is this: are they right?

Charles Ponzi's Scheme

On [Logical] Equivalence

In Newton's Law is F=ma?, explored the issue of whether or not this formulation was equivalent to Newton's actual statement of his 2nd Law. Today I want to further explore the topic of [logical?] equivalence. In general, I want to know what it means to say that two statements, $P$ and $Q$, are equivalent.

Junk Bonds: A Closer Look

So one of the questions I asked in Are Bond Yield Spreads Adequate? is whether or not junk bond spreads are adequate. I presented a simple model. The model predicted that returns on junk bonds would be about 2.27% in excess of treasuries. But the uncertainty in the model had a standard deviation of 2.36%. So if we were off by just 1 standard deviation, we would underperform treasuries.

But a model can't be better than the assumptions that one puts into it. I'd like to take a review of the assumptions I used in the model and change a few things.