Definition of Downside Risk
Downside risk, literally as the terms suggests, refers to the risk associated with the stock such that the stock price may have a downward movement resulting in a financial loss. In other words, downside risk is the possibility of losing money or value on account of any changes in the market and eventually a downward change in the stock price.
Explanation
While discussing downside risk, you may understand that the term “Risk” is basically a measure of standard deviation, whether in upward direction or a downward direction. Whereas downside risk measures standard deviation for only those stocks where return is/are below average or expected return.
The main difference is that standard deviation assumes that returns are symmetrical in nature, that is, the risk of a stock movement will be similar either in upward movement or in downward movement. Whereas downward risk is asymmetrical which takes into consideration that the risk associated in movement of stock price varies when it moves upward or downward.
This article we will deal with understanding the downside risk, what is means, how to calculate it and the measures of downside risk.
Formula
Downside risk can be calculated easily by way of a mathematical formulaas follows:
Downside Risk = Ö [å(Expected returns – Negative Returns)^{2} / No. of Periods]
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Note: For purpose of calculating downside risk, you only consider the negative returns i.e. returns which are less than the average or expected return. You ignore the positive returns.
As you can see, it can be calculated in simply few steps.
- Find out deviation in returns
- Segregate negative returns
- Square negative returns
- Sum the square of numbers so derived and divide by no. of periods
- Find the square root of the number arrived in step above.
Example
Let’s understand the downside risk with the help of an example. Suppose there is a company called Exumor Chanels Inc., with returns of past 15 years given in table below. For the purpose of this example, let’s take expected return to be 6%.
Year | Return % |
1995 | 8% |
1996 | 6% |
1997 | -7% |
1998 | -5% |
1999 | 3% |
2000 | 5% |
2011 | 4% |
2012 | 9% |
2013 | -2% |
2014 | -12% |
2015 | 3% |
2016 | 9% |
2017 | 15% |
2018 | 12% |
2019 | 7% |
Now, using the most commonly used method of semi-variance, to calculate the downside risk, we will compute the downside risk for investing in Exumor Chanels Inc.
- Step 1: Calculate deviation of actual return from the expected return.
Year | Return % | Expected return | Deviation |
1995 | 8% | 6% | 2% |
1996 | 6% | 6% | 0% |
1997 | -7% | 6% | -13% |
1998 | -5% | 6% | -11% |
1999 | 3% | 6% | -3% |
2000 | 5% | 6% | -1% |
2011 | 4% | 6% | -2% |
2012 | 9% | 6% | 3% |
2013 | -2% | 6% | -8% |
2014 | -12% | 6% | -18% |
2015 | 3% | 6% | -3% |
2016 | 9% | 6% | 3% |
2017 | 15% | 6% | 9% |
2018 | 12% | 6% | 6% |
2019 | 7% | 6% | 1% |
- Step 2: Now, segregate the ones with negative returns, and simply square them up and calculate the average return (sum of total return ÷ No. of years).
Year | Return % | Expected return | Deviation | Negative Deviation | Sq. of Negative deviation |
1995 | 8% | 6% | 2% | ||
1996 | 6% | 6% | 0% | ||
1997 | -7% | 6% | -13% | -13% | 1.69% |
1998 | -5% | 6% | -11% | -11% | 1.21% |
1999 | 3% | 6% | -3% | -3% | 0.09% |
2000 | 5% | 6% | -1% | -1% | 0.01% |
2011 | 4% | 6% | -2% | -2% | 0.04% |
2012 | 9% | 6% | 3% | ||
2013 | -2% | 6% | -8% | -8% | 0.64% |
2014 | -12% | 6% | -18% | -18% | 3.24% |
2015 | 3% | 6% | -3% | -3% | 0.09% |
2016 | 9% | 6% | 3% | ||
2017 | 15% | 6% | 9% | ||
2018 | 12% | 6% | 6% | ||
2019 | 7% | 6% | 1% | ||
Average return | 3.67% | 7.01% |
- Step 3: Finally, you find the square root of the number so arrived to find out the downside risk.
Measures of Downside Risk
- So now that you have understood what is a downside risk, it is clear that every investor will have its own specific set of risk qualities, investment strategies, and unique portfolio.
- As a widely accepted method, Value-At-Risk and semivariance are used to calculate the downside risk.
- Value-At-Risk means the loss of investments which the investor will have to bear, basis a given probability, market condition, and timeframe.
- Semi variance is the square root of semi deviation. A detailed understanding can be taken from the example discussed above.
Downside Risk Graph
Continuing with the above example, below you can see a graphical representation of what are the deviation of returns over the years as compared to the expected rate of return. The orange line, shows the expected return of the investor whereas the blue line shows the positive returns of the security over the years. Note that the grey line in the graph, wherever seen below the X-axis, depicts the negative deviation.
Management of Downside Risk
With a unique set of strategies and investments, every investor may consider the following parameters to manage in his stock or portfolio.
- Timeframe: How long is the investor planning to hold the security and accordingly strategize.
- Market Volatility: The market is very volatile and the returns on the security may be equally varied. Thus, as an investor, you need to be prepared for sudden changes in returns.
- Risk Appetite: Investors risk appetite will decide in drafting a proper strategy to plan for downside volatility in security.
- Safety: As an investor, you would like to minimise the downside risk to ensure the safety of your principal amount
- Expensive: Strategy planning may be a costly affair as you need to deploy funds for protecting against downside risk.
Advantages
Some of the advantages are given below:
- It is a preventive measure for investors to safeguard them against unexpected losses.
- Can be applied across various assets such as equity, debt, derivatives like futures and options, and such
- Keeps the investor prepared for the maximum loss scenario.
- Helps the investors in planning for hedging trades to hedge against the expected loss.
Disadvantages
Some of the disadvantages are given below:
- All calculation for downward risk is based on historical data. It assumes that the gain/loss trend will continue in a similar pattern.
- Based on assumptions and thus results can vary according to the assumption considered.
- There is a standard to follow on what shall be an acceptable level, as each investor shall have a different risk appetite.
- Mostly Experienced investors and traders will be in a better position to carry out hedging opportunities.
Conclusion
The downside deviation is basically a measure of calculating the risk of all the negative side returns of the expected or average return. There are various investors who measure the upside and downside deviation separately. And based on their preferences, the downside risk is used by them to know the scenario in event that there is a financial loss in the investments and the extent to which they can lose.
Remember, downward risk only gives a worst-case scenario and it is not that every expected investment will go downwards…!!!
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