## Evaluating strategy performance

### You will learn about the following concepts

- Strategy performance evaluation
- Compound Average Rate of Return
- Modified Dietz method

After a trader has chosen a strategy, backtested it and underwent prolonged simulations on demo accounts, he will ultimately begin using it in real-money trading. Although it might have yielded satisfying results during the simulation or for some time in real-money trading, this is not guaranteed to continue. Conditions on the financial markets are constantly shifting, especially fueled by the development of modern technology, thus rendering some trading strategies obsolete. In order to retain his competitive edge, a trader must regularly evaluate the performance of his trading system. And what better way to determine whether you are satisfied with your trading performance than to calculate your strategys returns and see if it is enough.

Calculating the returns of an investment (in our case the initial capital and time we have invested) can be done in several ways, depending on the time period, secondary withdrawals or deposits in the account etc.

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## Compound Average Rate of Return

The most common way to calculate the returns of an investment is the Compound Average Rate of Return. If it is over a single period and you are not adding or withdrawing funds from that account, then you would use a simple percentage change, like this:

(EOY – BOY)/BOY, where

– EOY is the value at the end of the year

– BOY is the value at the beginning of the year

Multiply the result by 100 and you will have the percentage change. A negative value indicates a loss in the value of the asset.

For example, if weve started with $1 000 and at the end of the year there are $1 500 in your trading account, then your annual return is: (1 500 – 1 000) / 1 000 = 0.50, or 50%.

However, we said that this calculation is on a single-period basis. If we are calculating the returns for lets say several years, the math is different because for example in the second year you will have returns on top of the first years returns. Thus you are looking for the compound return of your investment, not the simple return for a single year. Here is the formula:

– EOP is the value at the end of the total time period

– BOP is the value at the beginning of the total time period

– n is the number of periods

## Money flows

However, both of the return calculations above dont include any additional deposits during the tracked period, nor withdrawals. That is unlikely to work for most day traders, because this is their primary job and source of income, thus withdrawals from trading accounts will be needed on say, weekly basis, to cover everyday expenses. With money flowing in and out of your trading account, it would distort the performance evaluation done by the previous formulas. There are several methods to assess your performance while taking into account these variables.

The first formula is the so-called Modified Dietz method. It is based on the simple percentage change formula, but it is adjusted for the money inflows and outflows. This method is less accurate, but makes up with its simplicity. Here is how it looks:

(EOY – BOY – deposits + withdrawals)/(BOY + deposits – withdrawals)

Lets say for example that during the year we had to withdraw $200 dollars in April, but later in August we deposited $300. Our return would then be:

(1 500 – 1 000 – 300 + 200)/(1 000 + 300 – 200) = 0.36, or 36%.

### Time-weighted rate of return

The second method involves a more complicated two-step calculation but yields results with better accuracy. Its called the time-weighted rate of return. First you need to estimate the simple percentage change for each period (in our case for the three months to April, the four months through July, and the five months from August). A second calculation is then needed to incorporate all those returns in the longer period (in our case for the whole year). Lets do the math.

January – March – starting capital $1 000, ending capital, say $1 200, return rate is 20%.

April – July – starting capital $1 200, withdrawal $200, adjusted beginning for the period – $1 000, ending capital, say $1 100, return rate is 10%.

August – December – starting capital $1 100, deposit $300, adjusted beginning for the period – $1 400, ending capital $1 500, return rate is 7.1%

The second calculation looks like this:

– N is the total number of periods (in our case it is one year, thus 1)

– r is the return for that period

The calculation will then look like this : (1+0.2)*(1+0.1)*(1+0.071)-1 = 0.41372

Thus the time-weighted rate of return is 41.4%.