Performance – Geeky Math with a Purpose

The two geeky math problems below will show how reported performance can lead to confusing and misleading decisions.

I used investment performance for my examples, but this general concept can be applied to any situation:

When reviewing performance one must understand what is being measured.

The article Crime Rates Rise in Sandy-Sacked Areas includes the following quotes:

In the 100th Precinct, which covers the heavily damaged Belle Harbor and Breezy Point areas of Queens, crime is up 131% in November compared to a year ago…

Burglaries in the precinct have increased 1,200% so far in November compared with the same period of 2011, from 5% to 65%, according to police data.

My intention is not to dismiss the crime increase, only to state that without a reference point or definition of ‘crime’ we are unable to make appropriate decisions.

If ‘crime’ last year was .1% and is now .231%, that would be a 131% increase.

A large % increase does not always mean a large actual increase. As no reference point was provided, it would be irresponsible to make a decision based on the first bullet point.

The second quote provides some detail by defining the crime (burglary) and by providing an original rate (5%) and a new rate (65%). But, as it is only related to the overall crime rate, it still does not give readers the true picture.

The article sounds like people are more than 50% likely to get burglarized, but what they are really saying is that of the crime that is occurring more than 50% is burglary.

Crime is up and burglary is the main cause is the only thing we can derive from this article.

When the article provides numbered crime statistics for the neighboring 101st Precinct, the article states there were 8 burglaries last November and 57 so far this month. That doesn’t sounds particularly dangerous (or, unexpected) vs. “A 600% INCREASE!!! RUN FOR THE HILLS!”

But, I digress… I really didn’t intend to write about this, I just love writing about ‘shock’ journalism.

Now on to the two performance questions:

Question 1: Is it possible for an investment manager to show a client positive returns for a year, but at the same time lose their client’s money?

Question 2: Is it better to lose 50% then make 50% or make 50% then lose 50%?

First, Question 1: The answer is: Yes

Investment Managers calculate performance using formulas for time-weighted returns (TWR).

Without explaining the detailed math1, let’s just say that the general principle is to remove the impacts of cash flow on the returns. This is because the decision on when the client contributes and withdraws funds (in whole or in part) is out of the manger’s control.

The manager only wants to be judged on things they can control; investing the money under his/her purvey.

By example, a client gives an investment manager 100K on January 1st. The investment manager invests and makes 25% by the end of June. The client’s account is worth 125K. For fun, let’s also assume the SP500 was up, but only 20%. This shows the investment manager also out performed his/her benchmark.

The happy client now gives the manager an additional 1MM to invest. Over the next 6 months the market drops 25% and the investment manager’s portfolio drops 18%. Again, the manager has outperformed the market.

The investment manager can proudly state the following: “Last year I made my client’s 10%, while the market was down 10%.” Sounds great, right?

Let’s see how this particular client faired. After the second investment the client has 1.125MM (from an initial investment of 1.1MM), but loses 18% over the next 6 months and ends with $922,500.

So, while the manager claims positive performance, the client lost money ($177,500).

The Lesson:

When judging something; one should try to remove factors outside of its control.

If this example were real, the manager significantly outperformed their benchmark in both positive and negative markets.

Question 2: Is it better to lose 50% then make 50% or make 50% then lose 50%?

Answer: It makes no difference. But, what is more interesting (at least to me) is that in both situations you have lost money.

In any situation where you gain or lose an equal % over two reporting periods, you will lose money. Let’s look at some examples:

If you start with 100K and lose 50% you will have 50K. If you then gain 50%, you are gaining 50% on 50K so you end up with 75K.

If you start with 100K and gain 50% you will have 150K. If you then lose 50%, you are losing 50% on 150K so you end up with 75K.

In a more extreme example, if an investor lost 90% (100K to 10K), they would need gains of 1000% to break even.

The Lesson:

Controlling downside risk is critical as negative returns are far more impactful than positive returns.

1There are multiple methodologies, some with funny sounding names such as ‘Simple Dietz’ and ‘Modified Dietz’. Different formulas are used because getting an accurate valuation every time there is a cash flow is generally difficult (or, more often, impossible). The formula for Modified Dietz can be found here.