Frank the Financially Savvy Atheist - The F.S.A.

How much do you believe this statement? There is a 65% probability that the S&P 500 will be above it's current level (1479: closing at Aug 26th) at the end of the year? If you said, that's a load of crap, you are almost correct! Welcome to the world of Monte Carlo simulations.

With the markets reverting back to the mean of being actually volatile, instead of just kinda volatile, I thought it would be fun to do another Fun with Math post about Monte Carlo simulations and its application to finance.

The question we are trying to answer today is where will the S&P 500 be at end of the year? Will be it higher than it is currently, or will be lower? One purely quantitative way to answer the question is with a Monte Carlo simulation. As the wikipedia article states, these simulations are for "simulating the behavior of various physical and mathematical systems, and for other computations". There are a variety of applications in finance, and today we'll look at trying to estimate stock market returns.

First, we start with daaily S&P500 index data taken from Yahoo Finance, which goes back to 1950 or so. From there, we calcualate the daily returns of the index. Once we have that, we can say, if history repeats itself (randomly at that) we can kind of guess as to what the daily path of the S&P500 will look like. Here are two examples of what I mean.

The green line to the left is the actual index values and right where the green line and red line meets are the simulated values on the index based on the prior historical returns of the index. You can see that the green line ultimately diverges from the red line and ends up higher than the most recent close while the red line ends up lower.

Now, you run this simulation 100 times and get this result:



Once you're done with the simulations, you can then try to see what it's telling you. In these particular simulations, there were 65 scenarios where the ending value of the index was greater than the closing value of 1479 (hence the 65% probability mentioned earlier). Here is a graph of the % change from the current close.



Stats are as followed:
avg: 4.48%
median: 3.90%
std dev: 12.9%
max: 43%
min: -23%

So based on my simulation, I can say that the probability of the S&P500 ending up from its current value is 65%. Now the question becomes, how much stock (get it, hehe) should I put in these results? The results themselves aren't completely crap, but should be taken with a large dosage of salt possibly with a side of some more salt.

This was a rather unsophisticated simulation that didn't take into account the current economic landscape, interest rates, inflation or anything like that. It just threw some stuff on a wall to see what will take place. Not only that, but it was only done 100 times. It's hard to tease out any meaningful conclusions from a simulation that was only done 100 times. However, that's not to say that if I ran the simulation 1,000 or even 10,000 times that I would be 100x more confidence in the results, but it would be useful to start generating some conclusions from the output. But you would still suffer from the garbage in garbage out issue with any model/simulation.

All this is to say that your initial intuition with respect to the 65% was right all along :P.

Another brouhaha in the blogosphere, this time centering about the recent stock market volatility and some advice that Trent gave a reader. People, it's ok to disagree with popular, usually insightful, pf bloggers that you mostly agree with all the time :).

Heck, I've even gotten on his case before for his Mere Christianity post where he left comments like "If you really think that Christians are taken seriously at all or treated with any modicum of respect in mainstream popular culture, you’re kidding yourself."

I called bullsh*t and we had a minor tussle (if you can even call it that) and to this day he continues to be one of the most read blogs on my RSS feed because he's just that damn good of a writer. However, I still appreciate posts like mapgirl's response where she lays out some valid criticisms. So take for it what you will, and remember, don't listen to me either :P.

My little sister was visiting us over the weekend where she helped us do some paiting around the house. We started talking about an old friend of ours that had converted to Mormonism after graduating from high school. Then she made this particular comment: "Mormons aren't even real Christians anyway."

To which I retorted, bullsh*t. Of course it came down to how you define Christians or Christianity. My definition was essentially someone that believes Jesus was the Son of God. Her definition (which she wasn't really clear about) hinged on the fact that Mormons believed some weird stuff and therefore are not really Christians. After going back and forth, we agreed to disagree.

So what do others think, both Christians and non-Christians? Are Mormons Christian? If they are, why, and if they're not, why not? Also, if they're not Christians, then what are they?

I PASSED MY F@&%$& TEST!!!!! I PASSED MY GOD-DAMN F@%$&$* TEST!!! HOLY CRAP I PASSED.

Just don't remind me that I still have one more to go.

Surprisingly, two of my strong sections were Equity Analysis and Financial Statement Analysis. My other two strong ones were Derivaties and Quant Analysis, which was less surprising. My two worse sections were Ethics which was also surprising and Portfolio Management which I expected.

Now excuse me while I celebrate by dancing around in the office.

Wow. What a ride it's been in the financial markets. The topic du jour continues to be subprime, the unwind in leverage, and central banks injecting liquidity into markets around the globe. It's been the most volatility we've had in quite some time now. Cathy, substituting for JLP, over at allfinancial matters has a great round-up of different pf bloggers take on the current market. The responses range from people estatic about the market plunge (to use Cathy's word) to a surprising admission from Jim that he's liquidated an account due to the market volatility.

In either case, I wanted to respond to Cathy's question: What are your plans [for this market]?

Our plans for this market are two-fold:
1. To do nothing. To keep contributing to our 401(k) with the same asset allocation as before. Losing money sucks, but as long-term investors we'll keep slugging away for the long haul.
2. Do something...interesting. Allow me to explain.

Right now our Roth IRAs are both in money market funds with a pretty attractive yield. With the dislocation in the markets right now, I am of the conviction that we can profit off it by buying a mutual fund. I'm not going to say which one because inevitably someone is going to buy it, it's not going to work out and they're going to get mad at me. Now, I will only have myself to worry about if this doesn't work.

What's my rationale for buying the fund? The same given by the CFO of Goldman Sachs on the $2B injected into their fund: "This investment reflects our collective belief that the value of this fund is suffering from a market dislocation that does not reflect a fundamental value of the fund's positions"
And no, I wasn't one of the investors that contributed to the $2B :P.
So we are doing something a little more risky, but since it's a mutual fund, it's less risky. Does that even make any sense?

Essentially, we are trying to capitalize on the fact that EVERYTHING is being taken down with the current volatility, even things that are fundamentally sound. I'll be sure to keep you updated as to how this turns out. This is the first time we've tried anything of the sort with our personal money, so I'm feeling nervous to say the least.

The markets are down a lot today. The S&P was off almost 300 bps with the DOW down 283 bps and the Nasdaq down 216 bps. Why? Subprime. Yesterday, the markets were up, why? The markets had shrugged off subprime. And the day before that the markets were down, why? Suprime and credit concerns.

Does anyone really know why the markets are up or down on a given day? Make up your mind here.

Our net worth stands at ($5,412) for this month. We had two large expenditures for the month, our week long vacation and new carpeting for the majority of our home. The carpeting itself sets us back $1,300 but we are trying to save money by taking out the carpet ourselves and moving the furniture ourselves.

On the assets side we were down 149 bps. We unwound a balance transfer and paid our lumpy child-care payment to the au pair agency. My vesting percentage increased at work and my 401(k) balance is in the low 5 figures. The total market value of our 401(k) and both of our Roth IRAs is now in the ~$25,000 area depending on which way the market goes.

on the liabilities side we were down 103 bps as we paid off a significant portion of our total credit card debt (due to balance transfer) but had other balances tick up due to the large carpet purchase as well as the assorted vacation purchases.

I realize that our net worth is still negative, but I don't expect us to have a positive net worth anytime soon. In fact, it won't be positive for about a year or so. With my wife going back to school she will be taking on a significant amount of student loan debt which will set us back on the net worth side, but which will help her in terms of job prospects. That's not to say that we couldn't be doing a better with our spending, but right now I feel we are doing ok.