Greetings Cake Members!

This is Manu Sharma, Cake’s R&D Scientist, and I’m back with another glimpse into the inner workings of how we calculate all of the numbers you see on the site. Of particular importance to you, I assume, is how we arrive at the numbers related to the performance of your portfolio (i.e., how you have done managing your investments). 

Before you stop reading because of flashbacks to your high school calculus class, this will not be boring!  I don’t have a pocket protector, I don’t wear a short-sleeve dress shirt and too-big-for-my face glasses, and no, I don’t have tuna fish breath. And I guarantee you will learn something about yourself and the brokerage industry in the process.

Did you know, for example, that even though we are talking about math, something that is quantifiable like your portfolio returns over time, there is no universally agreed upon standard by the leading statisticians of our day for calculating this?  Crazy, I know.  Luckily I have been working with two respected finance professors, Lauren Cohen from Harvard Business School and Andrea Frazzini from the University of Chicago Graduate School of Business to help Cake arrive at a credible formula.

What is Portfolio return and how do we compute it? What is AAR and how do we calculate it? And what exactly does Risk mean? I’ve heard from many you and you are asking these important questions – and so let me discuss them briefly now.  For those with insomnia you can get all of the details to impress your friends at the next holiday cocktail party via PDF here and embedded below.

Portfolio Returns (a.k.a. Portfolio Performance)

It may seem a bit naïve to ask the question “What is Portfolio return?” But you will see it is not.  Simply put, when we talk about returns we are really talking about the percentage gain or loss of your portfolio value over time!   Now while this definition of portfolio return is correct, there are actually many ways to calculate it.  The three primary methods are:

1. Simple return – This tells you how much money you made by calculating the dollar change in your portfolio value divided by the total money invested. In any realistic portfolio where money moves in and out, this method should not be used because it assumes that all the money is invested at the beginning of the time period for which performance is being calculated.

>> It is a reasonable method to use only if you buy and let your portfolio just sit – no buys, sells or even dividends.

2. Time weighted return – This method calculates your return per unit time—e.g. each month or each quarter. It does not take into account when you actually added or withdrew your cash from the portfolio. Nor does it take into account how much money was in the portfolio during different time periods. Often known as the “Manager’s Return” this method is widely used to track the performance of professional investors, like mutual fund managers, who don’t have control over the timing of cash flow in a portfolio.

>> In other words, if you tell your broker to buy or sell on a certain day—and they support your move, then they don’t want to be held accountable for your timing decisions.

3. Money weighted return – Here we’re measuring your return on each dollar invested in your portfolio. Also known as “Dollar Return” or “Client’s Return”, this method takes into account how much money you put in your portfolio at different times, and then calculates a weighted return based on those factors.

>> Hello, this is the best way to figure out how your money is working for you.

All of these methods are correct mathematically speaking, but each can produce very different numbers– check out an example in the PDF.   For individual investors who make all their decisions on their own and have control over cash flow timings, the appropriate method to use is money weighted return – and so we use money weighted return to calculate your portfolio returns at Cake.

Still with me?  Tell you more, you say?  Okay!

Let’s start with Internal Rate of Return (IRR)
Working closely with Lauren and Andrea we evaluated all the different ways to calculate money weighted returns… and then decided on using the best, most rigorous and only exact method:  Internal Rate of Return (IRR).

Moving on… Average Annual Returns (AAR)
AAR is the average return per year you realized on your portfolio.  To compute your AAR, a lifetime return– including all of your data in our system– is calculated and then broken down into a yearly average.

And now the moment you’ve been waiting for: Risk
Risk is a bit of an abstract concept—it is a measure of the uncertainty of returns. Simply speaking, the less your returns fluctuate month to month, the lower your Risk.  Now from the mathematical standpoint, Risk is defined as the standard deviation of returns. Your Risk is the standard deviation of the monthly returns of your portfolio.

So, that’s the scoop.  All of these topics are discussed in much more detail– and with examples in the full article (PDF)… so please check it out.  We’re 300% committed to providing you with the most accurate, appropriate and relevant information so that you can better understand your portfolio performance.  Please let me know what you think!  I would love to hear from you.

I’ll be back to provide more insight into investment metrics in the coming months.  In the meantime, let’s keep the conversation going.

And remember, I have a Ph.D. in this stuff, so you don’t have to.

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