How to predict future security prices
I am tasked with predicting the likelihood that a security (variable annuity) will reach a certain value within a certain amount of time. I would like to be able to say that I am 90 percent certain that the value will at least be x in 2 years, 3 years etc. I am a new consultant for a securities consulting firm and am trained as a lawyer, so I haven't take any math classes since getting my undergrad in econ. Please answer as if you're talking to a young child or a golden retriever.
Ha, well that's not very helpful. This isn't the type of analysis we typically do. I want to run a time series prediction of the expected value of the security. What ever confidence interval. Any help or am I just going to get witty comments?
You need to run a Monte Carlo simulation. I assume this is a diversified equity portfolio with high embedded fees. You need to estimate the average market return, subtract fees, and run a number of iterations using a specified volatility. Even then, you will not be taking into account non-normal distributions, which will weaken your results. There are some other ways you can account for non-normal returns, but you will need to do some reading on that. I can't explain it in a post. This project is probably more difficult than you think if you have no background in it. If the annuity has other payoff structures besides just being long equities, you need to take that into account as well. The answer will be less than the value you start with for a 90% chance or greater. If there are no cash flows or resets (or other path dependencies), you should be able to do a closed-form solution using periodic assumed volatility (I.e. -- not annualized, but for multi-year periods) and solving for the z-score/return that meets the 10%ile.
By closed form solution, I mean something as simple as this: assume the average expected return is 8% and the expected vol is 20% annualized. To get the 2 year vol, multiply the vol by the square root of 2. Roughly speaking, 20% x 1.4 = 28%. For two years, 2/3 of your results will be between 16% +/- 28%; 95% will be between 16% +/- (2 x 28%). For three years, multiply by the square root of three and repeat. To get the result where exactly 90% or more of your results will be you need to look it up on statistical tables.
Keep in mind, these are far from perfect models, but this is probably what your boss is looking for.
This man knows his stuff.
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