In the

, the modified sharpe ratio is the key concept on which the performance of the participating traders is measured.In a nutshell, the concept is that **a trader who takes less risk will be placed higher in the competition than a trader that has taken more risk**, but achieved the same results.

This prevents one of the typical problems with trading competitions: some people try to take large risks and then hope for luck to do well in the competition's ranking.

This way, the competition is more realistic. Banks and institutions also do not want their traders to take excessive risk – after all, the first place is to manage a $100,000 account.

## Measuring risk has multiple facets

Measuring risk goes beyond looking at whether you risk no more than 2% of your account on any one trade. It also incorporates:

- How volatile are the assets you trade?
- The likely maximum that you can lose in a given time period

## Approaching risk the way banks and financial institutions do

There are many different approaches through which you can measure this success rate of a trading strategy and one of them is the so-called Sharpe ratio. In finance, this ratio is used to evaluate the outcome of an investment strategy related to its risk exposure.

For the trading challenge, a modified version of the Sharpe ratio is used.

### Advantages of the modified Sharpe ratio

- You can participate with any account size above €1,000 without a disadvantage.
- The best trader – not the most risk-taker – is rewarded.
- Deposits during the competition are possible.

### Calculating the modified Sharpe ratio

In the Trading Challenge we adopt a modified version of the

:**Modified Sharpe ratio = Rt / Σt**- Where
**Rt**is the rate of return of the portfolio up to time t; **Σt**is the risk of the portfolio up to time t – as measured by Value-at-Risk (VaR).

## Do I have to understand the modified Sharpe ratio to participate in the competition?

In practice, no. It's much more important that you follow your strategy that should incorporate a good risk and money management. If you have a great strategy and execute it well, you can get very good results in this competition.

You can compare it to the way the ELO in chess or the world ranking in tennis are calculated: it's not easy to understand in detail, but it doesn't play a big role: we know that it's a fair measure of performance.

## Example for calculating the modified Sharpe ratio

The most important thing to know about the modified Sharpe ratio is that the higher it is, the better the traders' risk-adjusted performance is.

Consider a trading strategy where we trade the EUR/USD:

On June 3, 2013 (day 1), we deposit 1000 EUR on our account and, at 14:00, we open a long position (buy order) in size of 1 lot for the opening price 1.3000 (1 lot being 100 000 units).

At the end of the day, the price has increased to 1.3020.

On June 4, 2013 (day 2), the value increases further and we close at 13:00 for a closing price of 1.3040. We made a profit of 307.21 EUR.

On June 5, 2013 (day 3), we open a short position of size of 2 lots at 8:00 for the value of 1.3030. At the end of the day, the price is 1.3035. Our equity decreases in the amount of 76.72 EUR.

The table below summarises our three-day trading:

Dates | Deposits | Equity | Open profits | Closed profits | Returns |
---|---|---|---|---|---|

3.6.2013 | 1000 EUR | 1153.61 EUR | 153.61 EUR | 0 | 153.61 EUR |

4.6.2013 | 1307.21 EUR | 0 EUR | 307.21 EUR | 307.21 EUR | |

5.6.2013 | 1230.59 EUR | -76.72 EUR | 0 EUR | 230.03 EUR |

### Calculating the sharpe ratio for our trading days

Now, to calculate the Sharpe ratio for our trading days, it is necessary to compute the first the level of the so-called 'Value-at-Risk' (VaR).

This is a statistical technique which risk managers use to measure the level of risk in an investment. It is quantified with three variables:

- Potential loss (in percentage or in monetary terms)
- The probability of potential loss (confidence level of either 95% or 99%)
- Time period.

VaR essentially asks the question: Considering a confidence level of 95% or 99%, what is the maximum percentage I can lose over the next day (or week, month, year)?

In the Trading Challenge, we use value-at-risk of 99% confidence level. This means that for a daily VaR of 1 lot (100 000) long position in EUR/USD which is 1%, we are 99% sure that the next day losses will be smaller than 1% x 100 000 USD = 1 000 USD. Conversely, there is 1% chance that losses will be bigger than 1 000 USD.

How do we do this? The table below shows the different daily and hourly VaRs in both dollars and euros:

Dates+Time | Hours | Price | VaR (USD) | VaR (EUR) | Risk |
---|---|---|---|---|---|

3.6.2013 (14:00) | 0 | 1.3 | 1000 | 769.23 EUR | |

3.6.2013 (23:00) | 9 | 1.302 | 769.23 EUR | ||

4.6.2013 (13:00) | 23 | 1.304 | |||

4.6.2013 (23:00) | 33 | 1.304 | 536.13 EUR | ||

5.6.2013 (08:00) (bought 2 lots) | 42 | 1.303 | 2000 | 1534.92 EUR | |

5.6.2013 (23:00) | 57 | 1.3035 | 714.32 EUR |

From the table above we can deduce the following:

- For 23 hours the value at risk was 769.23 EUR.
- For 19 hours the value at risk was 0.
- For 15 hours the value at risk was 1534.92 EUR.

The total time is T = 57 hours. Thus, the average VaR at T = 57 hours is calculated in the following way:

**1 / 57 x (23 x 769.23 + 19 x 0 + 15 x 1543.92)= 714.32 EUR**

### Putting it together

Now, we are finally ready to calculate the modified Sharpe ratio which, let us remember, was the following:

Rt / Σt

At the end of day 1, the Sharpe ratio is 0.2:

153.61 / 769.23 = 0.1996

At the end of day 2, the Sharpe ratio is 0.57:

306.75 / 536.13 = 0.5721

Finally, at the end of day three it is 0.32:

230.03 / 714.32 = 0.3220

You can download the historical VaR values for the last 260 trading days (last update: 13th of June), calculated as absolute values for 1 lot or 1 share respectively, by clicking the following:

## The modified Sharpe ratio: calculation for a simple Google share trade

Let us now look at how to use this ratio with an example of stock trading:

On June 3, 2013 (day 1), we deposit 1000 USD on our account and, at 14.00, we enter into a buy order of 10 Google inc. share for the price of 857.41 USD.

At the end of the day, the price has increased to 867.63 USD.

On June 4, 2013 (day 2), the value increases further and we close the position at 10:30 for a price of 868.84. We have made a profit of 114.3 USD.

On June 5, 2013 (day 3), we open a short position of 10 shares at 10:00 for the value of 868.25 USD. At the end of the trading day, the price is 859.61 USD. Our equity increases in the amount of 86.4 USD.

The table below summarises our three-day trading:

Dates | Deposits | Equity | Open profits | Closed profits | Returns |
---|---|---|---|---|---|

3.6.2013 | 1000 USD | 1102.2 USD | 102.2 USD | 102.2 USD | |

4.6.2013 | 1114.3 USD | 114.3 USD | 114.3 USD | ||

5.6.2013 | 1200.7 | 86.4 USD | 86.4 USD |

Now, as we know already, it is necessary to compute the value-at-risk before calculating the Sharpe ratio for our trading days. Again, we use a confidence level of 99% which means that the daily value at risk of a long position on 10 Google shares is approximately 1.7% (100%-99%). In other words, we are 99% sure that the next day losses will be smaller than 1.7% x (10 x 857.41USD) = 145.75 USD.

The table below shows the different daily and hourly VaRs:

Dates+Time | Hours | Price | VaR (USD) | Risk | |
---|---|---|---|---|---|

3.6.2013 (14:00) | 0 | 857.41 USD | 145.75 USD | ||

3.6.2013 (16:00) | 2 | 867.63 USD | 145.75 USD | ||

4.6.2013 (10:30) | 2.5 | 868.84 USD | 147.70 USD | ||

5.6.2013 (10:00) | 8 | 868.25 USD | 147.60 USD | ||

5.6.2013 (16:00) | 14 | 859.61 USD | 146.13 USD |

So, the total time is T = 14 hours. Thus, the average VaR at T = 14 hours is calculated in the following way:

1 / 14 x (2 x 145.75 + 2.5 x 147.70 + 8 x 147.60 + 14 x 146.13)= 314.87 USD

### Putting it together

Now, we finally have the factors to calculate the modified Sharpe ratio:

Rt / Σt

At the end of day 1, the Sharpe ratio is 0.70:

102.2 USD / 145.75 USD = 0.701

On day 2 at 10:30, the Sharpe ratio is 0.77:

114.3 USD / 147.70 USD = 0.773

Finally, at the end of day three it is 0.59:

86.4 USD / 146.13 USD = 0.591

You can download the historical VaR values for the last 260 trading days (last update: 13th of June), calculated as absolute values for 1 lot or 1 share respectively, by clicking the following:

## Want to learn more?

You can go to the following article to find out more about the standard sharpe ratio and how it is used:

## Why did we modify the Sharpe ratio?

The standard Sharpe ratio has a number of issues when applied to a trading competition:

- It works well only in the long term and frequent trading where we have a large number of observations – for example, one year of daily returns.
- Volatility and the standard deviation do not take into account the direction of a movement. For instance, an investor might see a sudden increase in a stock price as a favorable movement and she is not concerned with this type of movement.
- It is not necessary to take into account the risk-free interest rate for the trading competition at tradimo.

**For these reasons, we adopt a modified version of the Sharpe ratio.**

In our formula, returns (Rt) is calculated with no reference to the risk-free rate. In other words, this is done by taking into account the evolution of your portfolio's equity, minus the deposits and withdrawals from your account.

The risk exposure of the portfolio (Σt) is instead calculated by using the average of another risk measure: value-at-risk.

Compared to the standard deviation (σ), VaR better reflects the riskiness of the trading strategies as it assumes that investors are mostly concerned about the chance of incurring a big loss – and not about how much volatile their returns might be. Indeed, VaR addresses the following:

- What is the worst-case scenario?
- How much can I lose in a given time period?

In other words, how much 'value' am I putting 'at risk'?

## Now, back to the competition!

If you have any questions left, you can check our FAQ or our trading challenge discussion thread: