# Financial risk

**What is financial risk**

Financial risk refers to the uncertainty linked to the future value of any investment.

A financial instrument is deemed risky when the cash flow it generates is at least in part random, or cannot be calculated in advance with certainty. A classic example of a risky asset is equity security: it is impossible to know whether the price will increase or decrease over time, or if the company that issued it will periodically pay the dividends.

However, there are many other cases of financial risk.

Even bonds can be risky: indeed, the issuing company may go bankrupt and not return the principal or pay interest to investors. Even government bonds that mature in 10 or 20 years are risky: although it is highly unlikely that the government of an industrialized country will default (that is, be unable to pay the amount due), the inflation rate may unexpectedly rise, reducing the real value of the interest and the principal returned on maturity, and therefore the value of the security.

Seen from another perspective, making a risk-free investment means guaranteeing a certain cash flow. For example, the short-term government bonds of an advanced country (like US Treasury Bills or Italian BOTs are fully or almost fully risk-free. When they mature in a few months’ time, the risk linked to an unexpected increase in inflation is low, and we can be reasonably certain that the government will not fail to pay the principal and interest on maturity. Other examples of risk-free assets are demand bank deposits and short-term certificates of deposit.

**How risk is measured**

To precisely understand which methodologies are adopted to calculate the risk of an investment in the financial market, it is necessary to analyze three fundamental concepts: probability, expected value and variability.

**Probability**

Probability is the measure of the possible occurrence of a given outcome. An objective interpretation of probability is based on the frequency with which certain events tend to take place.

This means that without past experience on which to base the estimate of probabilities, it is not possible to obtain an objective measurement; in that case, it is necessary to rely on subjective assessments.

Subjective probability is the individual perception of the possible occurrence of an event. This may be based on the judgment of the individual or on experience, but not necessarily on the frequency with which the event took place in the past.

When probabilities are determined subjectively, different individuals can make different choices. For example, when we are asked to calculate the probability of finding oil in an unexplored area, we could attribute a higher probability to success than others, perhaps because we are more deeply knowledgeable of the project, or because we are oil industry experts and we can better leverage the information available to us.

Irrespective of the interpretation, probability is used to calculate another two important parameters that enable us to analyze risky situations: expected value and the variability of possible outcomes.

**Expected value**

The expected value is the weighted average of the values associated with the possible outcomes (payoffs), calculated using the respective probabilities as weights.

Therefore, the result is the central tendency, that is, the payoff that we would expect on average. Defining the “probability of” with Pr, we can express expected value as:

Expected value = Pr(success)x(value associated with success)+ Pr(failure)x(value associated with failure).

For example, supposing that we purchase a share of a company, we can realize earnings of €0.40 if it is sold to a large foreign group, otherwise we would earn only €0.20. Evaluating the probability of the purchase at 25% (or ¼), the expected value would be (¼)(€0.40)+(¾)(€0.20) = €0.25.

**Variability**

Lastly, variability is the extent to which possible outcomes of an uncertain event differ.

This is a highly important concept, and to understand it let’s look at an example in which we suppose that we need to select from between an investment of €10,000 in two securities with the same expected remuneration (€1,500).

Equity security A is issued by a new company, with a highly innovative product to be launched, and offers two payoffs of equal probabilities: if the product has a lot of success, the earnings are €2000. If instead it has little success, it is only €1000.

Instead, equity security B is of a company that has existed for many years, with a well-established market: the probability of earning €1510 is very high (0.99), but there is one probability out of one hundred that the company will fail, in which case the earnings would be only €510.

As already highlighted, the two securities have the same expected income:

- Security A – (0.5)(€2,000) + (0.5)(€1,000) = €1,500
- Security B – (0.99)(€1,510) + (0.01)(€510) = €1,500

However, the variability of the possible payoffs is different. To measure it, it is necessary to note that as the difference (negative or positive) between the expected and actual payoff increases, risk increases. This difference is called the deviation or spread. As this figure can also have a negative value, deviations are squared so as to always obtain positive values.

Returning to the example:

- Security A – (0.5)(€5,002) + (0.5)(-€5,002) = €250,000 The standard deviation of Security A is therefore equal to the square root of €250,000, or €500.
- Security B: Security B – (0.99)(€102) + (0.01)(€9,902) = €9,900. The standard deviation of Security B is the square root of €9900, or €99.50.

In conclusion, Security B is much less risky than Security A, given that the standard deviation of its remuneration is much lower. The concept of standard deviation naturally also applies in the case of more than two possible outcomes and outcomes with different probabilities.

**Risk management**

Managing risk means taking all measures necessary to control factors of uncertainty linked to an asset so as to limit the effects of potential adverse events.

In the case of the purchase or sale of financial instruments, risk management is based on the distinction between upside risk and downside risk.

As the purpose of the investment of savings is to obtain the highest return, the management of the risk of a financial portfolio will aim to limit the occurrence of negative events as much as possible and minimize the relative impact, while seeking not to hinder the occurrence of positive events. In other words, financial risk management consists of minimising downside risk without limiting upside risk too much.

Professionally managing the risk of a financial portfolio means proceeding with a series of assessments – relating to the individual assets included in the portfolio as well as the relationships between them, in addition to the portfolio as a whole – such so as to permit accurate planning of the risk to which the portfolio is exposed.

These analyses make it possible to define an ideal range of fluctuation for the portfolio – the “risk-return profile” – and establish the actions to be undertaken if its value fluctuates beyond the established threshold.

Therefore, risk assessment and analysis activities begin from the estimate of the probability and the possible impact of individual risky events, in order to develop a general framework of factors of uncertainty to which the portfolio is exposed. To conclude the analysis and assessment activities, the relationship between the opportunities and risks linked to the investment must balance the expectations and requirements of the investor.

**The return of a financial asset**

Individuals acquire and hold financial assets to enjoy the cash flow that they generate. To compare two assets, it is useful to consider this flow in relation to the value or the price of the asset itself.

The return of an asset is the total cash flow generated – including capital gains or losses – expressed as a fraction of its price.

When you invest your savings in shares, bonds, real estate or other assets, you generally hope to obtain a return higher than the inflation rate, so as to offset with the return the loss of buying power of the currency. For this reason, returns are often expressed in real terms, or net of inflation.

The real return of an asset is equal to the difference between the nominal rate of return and the inflation rate. Given that the majority of assets are risky, an investor cannot know in advance the returns that will be obtained in the subsequent year. For example, the price of an equity security may increase or decrease.

The expected return of an asset is the expected value of its return, i.e., the return which it should generate on average. In some years, the actual return may be much higher than expected, and in others much lower. But over the long term, the average effective return should be close to the expected return.

Different assets have different expected returns. For example, in October 2005 the real expected return of a US Treasury Bill was lower than 1 percent, while that of a portfolio of securities representing the New York Stock Exchange (NYSE) was higher than 9 percent. But if the difference in expected return was so significant, why were millions of people willing to purchase a Treasury Bill? Because demand for an asset depends not only on the expected return, but also on the risk: shares have a higher expected return than government bonds, but they are also riskier.

These data suggest that in general, the higher the expected return of an asset is, the higher the risk it entails. If the investment is properly diversified, this is true. As a result, the risk-averse investor must find the right balance between expected return and risk.

**The return and the risk premium**

The return of a financial security is defined thusly: the investor pays a certain purchase price, let’s say 100, and at the end of the year assesses his position using the market price of the asset, let’s suppose it’s 110, naturally taking into account dividends or coupons received during the year, for example, equal to 5. In this example, the final value of the investment is 115 (10 for the final price and 5 for the dividend) and must be compared with an initial investment of 100.

The total return is 15%. Is this a satisfactory return? It depends on the available alternatives. An alternative is without a doubt represented by an investment in an annual risk-free security, that offers a certain interest rate. Let’s suppose that the interest rate is 5%.

The return of 15% is, of course, higher than 5%, but it should be taken into consideration that the investment in the financial security entails a certain dose of risk. Instead of having a final price of 110, the security could have had a final price equal to 80 which, along with the dividend of 5, would have entailed an overall return of -15%. If the investment in the security is risky, it is not right to compare the final return of 15% with the interest rate of 5%, as the investor will be willing to invest in a risky security rather than in a risk-free security only if there is adequate profit.

On the one hand, it is necessary to take into account all possible scenarios of the risky return, calculating the expected return, and on the other hand calculating the alternative adding to the interest rate the sum necessary to offset the risk which is incurred, defined as the risk premium.

If for example there are only two possible return scenarios of the risky security, +15% and -15%, and if the probability of the first scenario is 90% and the probability of the second scenario is 10%, there is an expected return equal to nine-tenths of +15% and one-tenth of -15%, to obtain a final result of +12%. If the risk premium is 5% for example, then the expected return of 12% compares favorably with the sum of the interest rate and the risk premium, equal to 10%.

*Editor’s note: This article describes financial risk as a general concept. Although there are common EU laws, regulation may vary from country to country. For further information visit your Country’s Central Bank and Conduct Authority websites, or contact your bank or investment banker.*