One of the ways that risk is measured in finance is by calculating the standard deviation of returns. In statistics, standard deviation is a measure of the dispersion of returns from the average/mean value. Assets that have a higher standard deviation of returns are considered to be riskier because their returns tend to fluctuate more. As we know, higher risk creates the possibility of higher returns however the possibility of loss is also something that increases in likelihood and severity. Two data sets are illustrated in the graph below: the red line having the higher standard deviation of returns when compared with the blue line.
Notice how much more the returns of the higher standard deviation red line move when compared with the lower standard deviation blue line. Before we discuss the topics of standard deviation and diversification further, let’s have a quick recap on how to crunch the numbers.
Maths Recap
For this example, let’s use the monthly stock returns for BHP from the 1/5/2010 to the 1/8/2010 as a small data set.
| Date | 1/5/2010 | 1/6/2010 | 1/7/2010 | 1/8/2010 |
| Return | -1.5% | -6.6% | 7.7% | 5.0% |
Defining the following variables:
we can calculate the mean (average) and standard deviation of a data set by using the following equations:
Mean:
Standard deviation:
How diversification affects standard deviation
Taking the monthly stock returns between 1/5/2013 and the 9/4/2020 of BHP (BHP), Westpac (WBC) and Telstra (TLS) (Yahoo Finance 2020) the mean and standard deviation of the individual stocks returns are calculated as follows:
| BHP | WBC | TLS | |
| Mean | 0.294% | -0.668% | -0.403% |
| Standard deviation | 7.176% | 6.151% | 5.249% |
If we combine BHP and WBC into a stock portfolio with a 50/50 weighting, we see the following:
| Mean | -0.187% |
| Standard deviation | 5.392% |
The result of combining the 2 stocks into a portfolio has reduced the standard deviation of returns when compared with each stock individually. If we add TLS into the portfolio with a 1/3 weighting for each the mean and variance now look like this:
| Mean | -0.259% |
| Standard deviation | 4.413% |
Once again, we observe that the standard deviation has been reduced further; which demonstrates how adding more stocks to a portfolio (diversification) reduces the standard deviation (risk) of the portfolio’s returns.
Qualitative reasoning
The qualitative reasoning behind why increased diversification reduces risk is that individual companies (whose value is represented by their stock prices) are subject to idiosyncratic risks, which are uncertainties endemic to that company or sector (Chen 2019). Even if the same idiosyncratic risks affect multiple companies, each company will be subject to them in differing proportions, which means that all companies have a unique risk profile. For example, BHP is highly sensitive to commodity price movements, whereas a company like Telstra might only be affected to a small degree. This implies that the correlation of any stock when compared with another is never perfect, so by adding more stocks to a portfolio we are reducing the effect of each company’s idiosyncratic risk profile on the entire portfolio. We observe this mathematically, through reductions in the standard deviation of returns.
If we continue to add more stocks to our portfolio and produce of graph of standard deviation vs number of stocks it would look something like this:
On the far right of the graph, the stocks in the portfolio number in the thousands, so the standard deviation approaches that of the entire market. At this point we have removed the vast majority of idiosyncratic risk and are left with mostly systematic risk. Systematic risk refers to the risk inherent to the entire market (Fontinelle 2019). A very common index that is used to approximate this for the Australian market is the ASX300, which has a monthly returns standard deviation of 4.042% for the period 1/5/2013 to 9/4/2020 (Yahoo Finance 2020).
Standard deviation is not the be-all-end-all
While standard deviation is an excellent tool for mathematically describing the risk of a particular asset or portfolio, it is calculated is using historical data, which is inherently backwards looking. This means that you should not choose your assets based on standard deviation alone. It would be unwise to blindly believe that the events responsible for driving an asset’s value historically will continue to do so in exactly the same manner in the future. As investors we need to identify the risk factors that are driving the volatility of returns and try to predict how they will affect the asset going forward.
In addition to this, standard deviation only gives an indication of the dispersion of an asset’s historical returns, it does not indicate whether those returns are positive or negative. This means that it is possible to have 2 assets with the same standard deviation that move in different directions. This is why other metrics such as mean will also need to be taken into consideration.
What this means for you
Concentrated portfolios are riskier than diversified portfolios
Concentrated portfolios tend to be more risky than diversified portfolios due to the fact that they carry similar amounts of systematic risk but far more idiosyncratic risk. This means that owning a more concentrated portfolio creates the opportunity for higher returns but also higher losses.
Diversify across asset classes adequately
Diversification is a very effective tool for reducing volatility of returns. Qualitatively, the poor performance of individual assets within the portfolio will be compensated by the strong performance of other assets. As an investor you will need to diversify adequately such that your portfolio meets your individual risk profile as well as your requirements for returns.
Because it is so difficult to beat the market over the long term, personally, I believe that the majority of most people’s money should be invested in diversified funds that approximate common indices. If they want to be exposed to assets with high risk, they can set aside a small portion of their portfolio to do so – this should be an amount such that a total loss of the capital in this part of the portfolio will only have a minor effect on their capacity to achieve their goals.
Compare investment decisions against benchmarks
When presented with an investment opportunity try to compare its risk and expected return with that of a suitable benchmark to gauge how it fits in to your own risk profile. If you were to invest in an individual stock you should be aiming for it’s expected returns to exceed the performance of an appropriate index in order to compensate you for the additional risk that you are exposing yourself to. If it does not have a high probability of outperforming the index, it would be smarter to operate with the lower risk and higher return of the benchmark index.
Diversify over time
Using a technique like dollar cost averaging is an effective way to diversify across time. Picking asset price bottoms and tops (timing the market) is incredibly difficult so consistently buying chunks of an asset over time helps to reduce the cost base of a portfolio by causing you to buy more units when the price is lower.
Engineer your freedom
References
Chen. J, 2019, Idiosyncratic Risk, Investopedia, last viewed 16/4/2020 <https://www.investopedia.com/terms/i/idiosyncraticrisk.asp>
Fontinelle. A 2019, Systematic Risk, Investopedia, last viewed 16/4/2020 <https://www.investopedia.com/terms/s/systematicrisk.asp>
Yahoo finance, 2020, S&P/ASX 300 (^AXKO), last viewed, 15/4/2020,<https://au.finance.yahoo.com/quote/%5EAXKO/history?period1=1365724800&period2=1586649600&interval=1mo&filter=history&frequency=1mo>
Yahoo finance, 2020, BHP Billiton Limited (BHP.AX), last viewed, 12/4/2020,
<https://au.finance.yahoo.com/quote/BHP.AX/history?period1=1555037749&period2=1586660149&interval=1mo&filter=history&frequency=1mo>
Yahoo finance, 2020, Westpac Banking Corporation (WBC.AX), last viewed, 12/4/2020,
<https://au.finance.yahoo.com/quote/WBC.AX/history?period1=1555037749&period2=1586660149&interval=1mo&filter=history&frequency=1mo>
Yahoo finance, 2020, Telstra Corporation Limited (TLS.AX), last viewed, 12/4/2020, <https://au.finance.yahoo.com/quote/TLS.AX/history?period1=1368144000&period2=1586390400&interval=1mo&filter=history&frequency=1mo>