 # The Relative Risk Ratio: An Alternative Way to Manage Risk

Without complicating the subject too much, and engaging in a discussion which may generate results that are inapplicable in the context of the common tools possessed by a retail trader, we can identify three variables in the relative risk ratio equation that determines how risky a hypothetical forex portfolio is. By risk, we focus on the maximum drawdown our portfolio may have to survive, if matters don’t progress in the anticipated direction. The variables in question are leverage, trade size, and volatility. Since the total return is dependent on leverage and trade size (both of which are determined by the trader), and on the volatility of the initiated trade (which is unknown, and determined by the market), it is not difficult to see that these three provide a simple yet effective definition of risk.

## Mathematical description of relative risk ratio in a forex portfolio

Proceeding from the above reasoning we can reach at a mathematical description of the risk assumed in a forex portfolio. It is important that our forex portfolio not be heavily skewed toward any currency pair. For instance, the distribution of currency pairs is more like 60% EURUSD, and 40% USDJPY, and not 90% USDJPY, and %10 USDCHF.

Relative Risk = (Leverage x Trade Size x (

Average Volatility of the Portfolio/Volatility of S&P 500)) / Account Equity

We take not the volatility of a pair itself, but the ratio of its volatility to the volatility of EURUSD or S&P 500 for the purpose of reaching a definition of relative risk. There is no credible relationship between historical and future volatility, so assessing risk on the basis of past patterns would not be very useful. It is possible to assume, on the other hand, that even as volatility itself changes, the relationship between the volatilities of two currency pairs changes slower, due to the underlying fundamental factors that determine it. Using this approach may allow us to gain an idea on how risky our portfolio is in reference to a base pair which we regard to be highly liquid and reasonably stable.

We prefer this ratio to remain as small as possible. We also want to determine a ceiling value for it, so that the risk of trades that we initiate does not breach a predetermined value. Needless to say, it is not very sensible to identify a numerical value, and to claim that all trades stay beneath that ceiling, in order to maximize returns and minimize risk. But while it may not be possible to achieve that purpose, we can use the relative risk ratio (RRR) to create a plan for reducing or increasing the riskiness of our portfolio depending on the trading strategy that we employ.

## An example in carry trading

In example, let’s suppose that we are carry trading, and on the basis of our analysis, we assume that the market presents great opportunities for a carefully managed carry trade portfolio held over the long term. Although we know what kind of pairs we will purchase while constructing our portfolio, we do not know exactly which pairs we should be purchasing (on the basis of the assumption that the most lucrative carry trade pairs present similar fundamental patterns.) Furthermore, if we want to adjust our portfolio in response to news events and various data releases, it is difficult to determine how much of a pair we should buy in order to replace the less profitable position(s).

In order to do this, we first determine the ceiling for the RRR, described above, and then we subtract the risk value of the liquidated trade from it. In more concrete terms, supposing a hypothetical maximum RRR of 15, and a relative risk value of 3 for the liquidated position, we find that our reduced portfolio has a RRR of just 12, allowing us to purchase any amount of the replacement pair provided that its risk ratio does not exceed 3. Or,

(Replacement Pair Leverage x Replacement Pair Trade size x (

Average Volatility of the Pair/Volatility of S&P 500)) / Total Account Equity < 3

You can even use this method while trading with multiple accounts with differing leverage ratios for each of them, in accordance with different trading strategies. In order to ensure that your risk is always under control, make sure that the risk ratio of any liquidated position is equal to, or greater than that of the newly initiated trade.