Follow-up On Investment Poll

In an earlier blog I presented a poll with three alternatives (if you haven't taken the poll, see here). There's some observations at the above blog as well as at Fool and OSV.

My 1348% Per Year Investment!

So several years ago I made a very small investment which has returned quite well. I made my money back within a few months and the rest was pure profit.

Altogether, I estimate that my returns have been 1348% per annum.

Financial Mathematics: Financial Calculators

Actually working out most of these formulas by hand can be time consuming. In some cases, there is not a slick algebraic solution in which case you'll have to use brute force calculations or some approximation technique (to find the interest rate). So here's a quick review of some alternative ways do actually do the calculations.

Financial Mathematics: The Rule of 72

At some time or another you've probably heard of the "rule of 72". I'm going to give a derivation of this result and show how good of an approximation it is.

On GMO's 7-Year Asset Class Return Model

Every month GMO gives forecasts for several different asset classes (sign up for free to access these). What I'm going to do a quick look at is the model they use to derive these projections.

Poll: Which of these investment options do you prefer?

So the following is a poll I'd like to conduct. Feel free to post thoughts on your reasoning. I'll present three investment alternatives. Your job is to order them by preference.

Financial Mathematics: Continuous Compounding Interest

Earlier we set up the basic compounding (discounting) factor for when interest is compounding at smaller intervals than 1 year:
$$\left(1+\frac{i}{m}\right)^{nt}$$
where $i$ is the interest rate, $n$ is the number of divisions in a year and $t$ is time expressed in years.

Next we're going to suppose that compounding occurs, instead of annually, quarterly, monthly or even daily, but rather in a continuous manner. This means that our time interval goes to 0 or the number of intervals in the year is infinite.

Financial Mathematics: Periodic factor, APR and APY

So in the first piece on the Time Value of Money, we looked at scenarios in which interest was compounded annually. But interest is not always compounded annually. Some assets compound semiannually, quarterly, monthly or even daily. So we need to develop some tools to deal with these.

To begin with we will introduce some terminology.

Financial Mathematics: Time Value of Money

One of the critical ideas that drives much in financial mathematics is known as the Time Value of Money (TVM). So I think it's important to start here. In fact, if you do not understand TVM, you will not understand the remainder of this series as TVM is an implicit assumption in most of these models.

The key idea behind TVM is that a dollar today is not worth the same as a dollar tomorrow. Part of what motivates this idea is postulate about human behavior.¹ That idea is that human beings prefer to have something (money) now rather than later. As a result, money in the future is worth less today than it is in the future.

Financial Mathematics: Table of Contents

This is the beginning of a series of blogs on financial mathematics. The purpose will be to motivate the techniques used as well as derive explicit results. The presentation will be for those interested in seeing the logic behind the equations and what assumptions are made to derive them.

Feel free to bookmark this page as I update content.

You are more than welcome to post feedback on the series. My goal is to explain the concepts in a way that promotes understanding. If there are any errors, confusing concepts or anything else that needs clarifying, feel free to let me know.

Table of Contents

1. Time Value of Money
1. Periodic Factor, APR and APY
   
2. Continuous Compounding Interest
   
1. The Rule of 72
2. Annuities
1. Loans - Annuity Immediate
2. Loans - Annuity Due
3. Geometric Progression
4. Perpetuities 
3. Bond Valuation
4. Stock Valuation

Appendix

1. Financial Calculators
2. Sequences and Series
3. Geometric Series  
4. Flow of Funds Table
5. Statistics - Expected Values  
6. Statistics - Moments

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