In traditional investing, risk is viewed as volatility or standard deviation of the asset’s marked to market value. Standard deviation tells you how much an investment’s value will fluctuate from the average return. The more volatile the investment is likely to swing (both positively and negatively) around it’s own historical average, the more risky an investment or asset class is.
For example, Chart 1 below shows the normalised returns of Global Equities, as represented by MSCI World Index, versus Global Bonds, as represented by Citigroup Broad Investment Grade Bonds Index.
If you had invested $100 in both Global Equities and Global Bonds for the past 10 years, your portfolio value of either would be fairly similar, which is $168 for Global Equities and $165 for Global Bonds. (pretty dismal annualised returns per unit risk for Global Equities but that’s another story altogether) However, Global Equities is more volatile than Global Bonds and hence more risky by definition. The standard deviation of a time series of daily returns for Global Equities is 2.53% versus 0.50% for Global Bonds.
There are many more traditional measures of risk such as Value-at-Risk or Conditional-Value-at-Risk, which is an extension of VAR. These measures are widely used by the vast majority of investors for many years now.
However the most important and relevant risk to me when I trade is the Risk of Ruin. There were many sources of inspiration and influences (the “Market Wizards†type of traders and successful fund managers) through the years in shaping my thoughts on trading and this concept of looking at risk as the “risk of losses of trading capital†has been one of the most important.
So how do we quantify the risk of ruin? I came across these 2 methods as described below. They were referenced from D.R. Cox and H.D Miller in “The Theory of Stochastic Processesâ€.
For fixed trade size without dynamic position sizing (i.e. fixed trade size regardless of trading capital changes)
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.
For fixed trade percentage (e.g. 2% of capital per trade)
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
ln(1-z) = natural logarithm of (1-z)
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.
You may wish to incorporate these calculations in your money management tools to give you an idea of the risk of ruin which is so important in trading. Live to trade another day. It is all about survival in this game!
For example, Chart 1 below shows the normalised returns of Global Equities, as represented by MSCI World Index, versus Global Bonds, as represented by Citigroup Broad Investment Grade Bonds Index.
If you had invested $100 in both Global Equities and Global Bonds for the past 10 years, your portfolio value of either would be fairly similar, which is $168 for Global Equities and $165 for Global Bonds. (pretty dismal annualised returns per unit risk for Global Equities but that’s another story altogether) However, Global Equities is more volatile than Global Bonds and hence more risky by definition. The standard deviation of a time series of daily returns for Global Equities is 2.53% versus 0.50% for Global Bonds.
Chart 1: Normalised Returns For Past 10 Years For Global Equities & Global Bonds
There are many more traditional measures of risk such as Value-at-Risk or Conditional-Value-at-Risk, which is an extension of VAR. These measures are widely used by the vast majority of investors for many years now.
However the most important and relevant risk to me when I trade is the Risk of Ruin. There were many sources of inspiration and influences (the “Market Wizards†type of traders and successful fund managers) through the years in shaping my thoughts on trading and this concept of looking at risk as the “risk of losses of trading capital†has been one of the most important.
So how do we quantify the risk of ruin? I came across these 2 methods as described below. They were referenced from D.R. Cox and H.D Miller in “The Theory of Stochastic Processesâ€.
For fixed trade size without dynamic position sizing (i.e. fixed trade size regardless of trading capital changes)
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.
For fixed trade percentage (e.g. 2% of capital per trade)
R= Risk of losing z fraction of the trading capital in percentage terms (probability)
e = Base of natural logarithm, 2.71828
ln(1-z) = natural logarithm of (1-z)
z = If we want to calculate the risk of losing half the account, input 0.5
a = mean return of the trades, must be same time frame as d. For example if daily mean returns are used, then use standard deviation of daily returns. If weekly mean returns are used, then use standard deviation of weekly returns.
d = standard deviation of returns, must be same time frame as mean returns mentioned earlier.
You may wish to incorporate these calculations in your money management tools to give you an idea of the risk of ruin which is so important in trading. Live to trade another day. It is all about survival in this game!
Editors’ Picks
EUR/USD trims gains, back below 1.1800
EUR/USD now loses some upside momentum, returning to the area below the 1.1800 support as the Greenback manages to regain some composure following the SCOTUS-led pullback earlier in the session.
GBP/USD off highs, recedes to the sub-1.3500 area
Following earlier highs north of 1.3500 the figure, GBP/USD now faces some renewed downside pressure, revisiting the 1.3490 zone as the US Dollar manages to regain some upside impulse in the latter part of the NA session on Friday.
USD/JPY sticks to gains above 155.00, over one-week top ahead of US data
The USD/JPY pair gains positive traction for the third straight day and climbs to over a one-week top, around the 155.35-155.40 region. Data released early today showed that Japan’s key inflation gauge eased to the slowest pace in two years, tempering expectations for an immediate policy tightening by the Bank of Japan.
Editors’ Picks
EUR/USD: US Dollar comeback in the makes? Premium
The US Dollar (USD) stands victorious at the end of another week, with the EUR/USD pair trading near a four-week low of 1.1742, while the USD retains its strength despite some discouraging American data released at the end of the week.
Gold: Escalating geopolitical tensions help limit losses Premium
Gold (XAU/USD) struggled to make a decisive move in either direction this week as it quickly recovered above $5,000 after posting losses on Monday and Tuesday.
GBP/USD: Pound Sterling braces for more pain, as 200-day SMA tested Premium
The Pound Sterling (GBP) crashed to its lowest level in a month against the US Dollar (USD), as critical support levels were breached in a data-packed week.
Bitcoin: No recovery in sight
Bitcoin (BTC) price continues to trade within a range-bound zone, hovering around $67,000 at the time of writing on Friday, and falling slightly so far this week, with no signs of recovery.
US Dollar: Tariffed. Now What? Premium
The US Dollar (USD) reversed its previous week’s decline, managing to stage a meaningful rebound and retesting the area just above the 98.00 barrier when tracked by the US Dollar Index (DXY).
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