## Friday, December 28, 2007

### A Random Walk Down Wall Street

On average only about 20% of the cost of bringing a product to market is spent on research, development, and manufacturing. The rest is the sales and marketing expenses.

This varies by industry quite a bit, and nowhere the sales and marketing share of the pie is so pronounced as it is in the finance industry. Ever heard of the multi-million dollar Christmas bonuses on the Wall Street? Yes, the very same people who create all these wonderfully complicated schemes that they push on you in exchange for large commissions!

If I had to pick one thing that I have learned in business school to keep, and forget everything else, the class I would choose would be the class in risk and derivatives - the financial instruments which allow factoring out the trend out of the stock to focus on it's purely random component, or the random component to focus purely on a trend, etc. And the most interesting thing I learned there is CAPM, or Capital Assets Pricing Model.

The theory is simple enough for a first-year college student to understand. It goes approximately as follows.

Let's say we have a portfolio of all stocks and other securities in the universe with spot (current) prices Ei, i = 1..N. Let's say the standard deviations of the distribution of the prices of these securities are Si. The weights in which they are present in the portfolio are wi, w1 + w2 + w3 + ... + wN = 1.

The risk of a stock or a portfolio is quantified by its standard deviation. The standard deviation of a portfolio is a square root of quadratic polynomial of its weights - a convex function on a plane where we have standard deviation on a horizontal axis, and return on a vertical.

Let's now consider a combination of risk-free investment (cash, the theory assumes that you are a big player and you can borrow and lend at very close rates) which pays interest rF, and the some portfolio with some combinations of fixed weights. Using these 2 financial instruments, you can construct a combination portfolio that has a given return between rF (you have all your money in cash) and infinity (you have borrowed an infinite amount of money, and bought an infinite amount of the aforementioned portfolio with it).

On our graph the returns for a given risk all will lie on a line connecting the point representing risk-free cash (0, rF) with the point representing our portfolio (Sw1w2w3w4...wN, Ew1w2w3w4...wN). Because the graph of all possible portfolios is convex, there exist a single point (a tangent to our set of all possible portfolios) which has all other lines passing through all other possible portfolios below it.

Courtesy of Wikipedia:

Points on this line represent the most effective investments - for a given risk, they carry maximum return, and they achieve any given level of return with the minimum risk.

The conjecture that won a Nobel in Economics is that this point is the current "market" portfolio - i. e. all of the market, of which most people consider SP500 to be a "good enough" representation.

What does this mean for a casual investor and finance professor alike? That regardless of what you're being told by your broker, the best investment you can buy is and SP500 index fund. The rest is basically made to maximize the salesman's commissions and fund manager's income (Vanguard SP500 fund expenses ratio is 0.19%, as compared to 1.5% of an average "managed" index fund).

An aside:
Dogbert is talking to Alice, who's going to a trade show.
Dogbert: "To be successful at the trade show, you'll need a trade show booth from the Dogbert Trade Show Booth Company. For maximum profts, I recommend the deluxe model."
Alice: "How will the deluxe model maximize my company's profits?"
Dogbert: "Oh, so now this is about *your* company?"

Another aside: The finance professors I personally know from UW's business school invest either exclusively or primarily in SP500.

But wait! you'd say. There are plenty of stocks and funds that outperform SP500 by a large margin! AAPL! GOOG! The energy fund! The gold! The point here is that they do it at a considerable risk, which is higher than can be delivered by the efficient portfolio. Measuring return without the attendant risk is meaningless.

So if you want to achieve a greater return, you can borrow the money from the bank, put them in the index fund - and it will be less risky for any level of return than any stock or mutual fund.

More on CAPM here: http://en.wikipedia.org/wiki/Capital_asset_pricing_model