Portfolio Performance | Cake Financial by Cake Financial

Talking about Portfolio Performance By Manu Sharma, Cake’s R&D Scientist

Greetings Cake Members! It may seem a bit naïve to ask the question “What is Portfolio return?” when, quite simply put, it is the percentage gain or loss of your portfolio value over time! Well—while the above definition of portfolio return is correct, there are actually many ways to accurately calculate it; there is not one unique and universal method. This is best illustrated by the following examples: Consider you buy 100 shares of Company A on Jan 1 2005 at $10.00 which grow to $12 on Dec 31 2005. • Your return for the period is 20% (100 x 12 – 100 x 10)/(100 x 10). Very easy. • This is called a simple return. A simple return is the difference between the final portfolio value and the initial investment (the dollar change in portfolio value) divided by the initial investment. Simple return doesn’t take into account timing of cash flow – i.e. it assumes that all of your money is invested at the beginning of the period. Simple Return = (Final Portfolio Value – Initial Investment) / Initial Investment You feel that Company A is an excellent investment, you are very happy with your 20% return over the last year, so you buy another 1000 shares at $12 on Jan 1, 2006. Unfortunately, the company does not do as well as you thought it would, and the share price on Dec 31 2006 is down to $11. The simple return for 2006 is -8.3%. This is where it gets interesting. What was your return for 2005 and 2006? • •

Calculating the simple return for your performance 2005-2006, we find that the simple return is -6% You invested $13,000 — $1000 on Jan 1 2006 and $12,000 on Jan 1 2007 — and lost $800 or 6% over the course of the entire period

On the other hand, one can say that you made 20% in 2005 and lost 8.3% in 2006, so your total return is an average of the two simple returns, taking into account the compounding using a geometric average: • •

(1 + 20%) x (1 - 8.3%) – 1 The 2-year compounded return—or time weighted return—turns out to be 10 %

This calculation is perfectly legitimate; in fact, time weighted calculations are common practice. Nevertheless, let’s spend a moment looking at this calculation objectively:

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• • •

We agree that you made 20 % in 2005 and lost 8.3 % in 2006. However, you only invested $1000 in 2005, but $12,000 in 2006. So, in monetary terms, you made $200 in 2005, but lost $1000 in 2006. Overall you lost $800…yet your return over two years is 10%, based on the timeweighted calculation! That’s incredible—you lost money and you have a positive return!

So what’s wrong here? Nothing – as long as you’re comfortable using the time weighted return method. This method is widely used when assessing the performance of professional investors – like mutual fund managers (since they don’t want to be held accountable for decisions a client may make that has bad timing). You wouldn’t be very happy if your money manager told you that you made 10% over the last two years when you actually lost money! I know I wouldn’t! So is there an alternative? Indeed; it’s known as the money weighted return method. Money weighted return takes into account how much money you put in your portfolio at different times, and then calculates a weighted return based on those factors. If we re-calculate the above example using money weighted return, you’ll find a calculation that more accurately reflects your portfolio value after two years: the money weighted return is -12.5 %. Here we have an interesting situation. We have three very different returns for the exact same portfolio! Simple Return

= -6 %

Time Weighted Return

= + 10 %

Money Weighted Return

= -12.5 %

Which one is correct? They all are – mathematically speaking. Which one should we use? Clearly, the time weighted return is not suitable to use, as it yields counterintuitive results – it is appropriate to assess performance of investors who do not have control over cash flow timings, like a fund manager, who buys and sells whenever instructed by the client to do so. The simple return is a very crude estimate of your return and should never be used, since it does not take any cash flow timings into account. As mentioned above, it assumes all the money in the portfolio was invested at the beginning of the period. For individual investors who make all their decisions on their own and thus have control over cash flow timings, the appropriate method to use is money weighted return.

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In order to calculate the return correctly, one needs to consider the fact that most of the money ($12,000) spent only half the time in the portfolio (Jan 1, 2006 to Dec 31, 2006), so the money weighted return is different from the simple return (-6 %) and is almost double that value. You lose money at a higher rate if you have less time to lose it. We use money weighted return to calculate your portfolio returns at Cake. There are several different ways to calculate money weighted returns (depending on how much time you want your computer to spend number crunching) and we use Internal Rate of Return (IRR). • IRR takes all the cash flows in and out of a portfolio (buys, sells, dividend, reinvestments) and calculates an effective return for a specific time period. • IRR is the only mathematically exact and rigorous way to calculate money weighted return. o All other formulae used to calculate money weighted return (like Simple Dietz, Modified Dietz etc.) are approximations, which can fail under certain circumstances – and so, while expensive, we use the more exact IRR method. Why is IRR costly? Because IRR cannot be solved analytically – there is no IRR formula where you plug in the values and get the result, one must use numerical methods to find the solution. This means that one has to “guess” or “estimate” the solution and iteratively solve the IRR equation until the correct solution is obtained. Essentially, one starts with an estimated return and plugs it into the IRR equation to calculate the final value of the portfolio. The difference between the actual final value (which we know) and the calculated final value tells us whether our guess is an overestimate or and underestimate of the correct IRR. One then adjusts the estimated return in the appropriate direction (if the guess is an overestimate of the correct solution then reduce the guess and vice versa). The process is repeated until the calculated value of the portfolio and the actual value of the portfolio are the same. That’s the IRR solution. Of course, I have oversimplified the process here, but you get the picture! This iterative process is what we do in order to provide you the most realistic look at your portfolio performance. To get this done, for each member, we: • Conduct about 20 iterations to find an IRR solution for your unique portfolio • Perform about 50 IRR calculations per user for all metrics that you see on your Cake homepage • In total, that’s about 1000 calculations for you each day We then use the returns computed using IRR for calculating all user metrics like Average Annual Return (AAR) and Risk, as well as Month to Date (MTD) return, Year to Date (YTD) return, 5 day return, 35 day return, 1 year return, 5 year return. Rank is also calculated using these key metrics, as you can read about it my first blog post. To learn more about the different ways of computing average returns over multiple time periods, check out this great website dedicated to methods used in analyzing investment performance as well as Wikipedia's description of Rate of Return. Interested in more detail about IRR? I recommend checking out this valuable resource.

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Average Annual Return (AAR) Average Annual Return is the average return per year you realized on your portfolio. The average is a geometric average to ensure that compounding is taken into account. To compute your AAR, we first calculate the return you have attained over the lifetime of all your data that we have in the system. The lifetime performance is translated into a yearly average. Here is an example: Suppose you have three years worth of history and your return for this period is 55 % then your average annual return would be 15.7%. The equation for this is: (1 + 55%) = (1+AAR)3 and the solution is AAR = (1+55%)1/3 â&#x20AC;&#x201C; 1 = 15.7%

Risk Risk is a bit of an abstract concept. Simplistically speaking, it is a measure of the uncertainty of returns. Consider Company A with yearly returns of 13%, 20%, -14% and 11% respectively, with an average annual return of 6%. Now Consider Company B with yearly returns of 6.1%, 5.9%, 7% and 7.6%, also with an AAR of 6%.

Year 1 Year 2 Year 3 Year 4 AAR

Company A 13 % 20 % -14 % 11 % 6%

Company B 6.1 % 5.9 % 7% 7.6 % 6%

Which would you consider more risky? A or B? Clearly, if you invested in Company A, you would have made large amounts of money in some years, but also lost large amounts in other years. If you had invested in Company B, you would have made money at a lower, but steadier rate. Over four years, you would have the same amount of money regardless of which company you invested in. However, a steady gain is considered less risky than a widely fluctuating one. Mathematically, Risk is defined as the standard deviation of returns. The standard deviation measures the spread of a distribution about its mean. In other words, it is a

ÂŠ 2007 Cake Financial Corporation

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measure of how scattered numbers are around their average. The returns can be monthly – which result in monthly Risk, or yearly – which result in an annual Risk. The conversion from one to the other is straightforward. (Monthly Risk x 12 = Annual Risk). We compute two types of Risk: 1. The first one is the historical risk of a portfolio based on monthly returns. This is used in calculating a user’s rank. It is calculated from a portfolio’s realized historical monthly returns. 2. The second one is a portfolio’s current risk. The risk that you see on your Cake homepage is your current risk. It is the risk based on the historical monthly performance of the stocks that you currently hold. In other words, it is not the risk based on your historical performance, but based on the historical performance of your current holdings. Suppose you held AAPL and OIL for the last year, and sold them yesterday, and bought EEM and FCNTX. Your historical risk, which is used to rank you, is the standard deviation of the monthly returns of your portfolio over the last year, which comprised of AAPL and OIL. Your current risk, what you see on your homepage, is the standard deviation of the monthly returns of your current holdings, in this example, EEM and FCNTX.

The risk icon that we use to illustrate a user’s current risk is a translation from the mathematical standard deviation of the current holdings to a scale from 1 to 5. The users with the 20% lowest standard deviation get the first level, low. The next 20% get medium-low and so on until the last 20% that get assigned a high risk level so our assigned current risk is relative to the other users on Cake and not an absolute risk measure.

Portfolio Return and Risk are the fundamental metrics that we use as the basis for all metrics seen on Cake. I’ll be back to provide more insight into investment metrics in the coming months. In the meantime, let’s keep the conversation going… Questions, comments? Please let me know. Post to the blog or email me (Manu Sharma) at feedback@cakefinancial.com. Thank you!

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