## Risk Management – Part B

*Manolis Anastopoulos @ University of Leicester - Risk Management*

**2.1 Return and risk**

**2.1.1 Return**

Undoubtedly, the value of a claim is determined from its return (cash flow) over the holding period. Certainly, the *level *of the risk that is associated with the expected return is negatively related to the value of the claim. For example, a cash flow prepared for a vessel of 25 years of age has incorporated a great risk or uncertainty (expected earnings are very sensitive to a possible downturn of freights because of the vessel’s age), which results in lowering the value in question.

Finally, what investors actually consider is the **present value (PV)**, which according to the basic valuation model, states that the value of any asset is ‘the present value of all future returns (cash flows) it is expected to provide over the relevant time period.’

More specifically, we can calculate the PV of a dated fixed-interest security (*P*DFIS), using, as stated in his book (King 1999), the following equation:

*C: Annual coupon payment*

*n: A maturity value*

*M: Years to maturity*

*r1, r2 and r n: The annual rates of return required on loans of one, two and N years to the security issuer.*

In many cases, investors anticipate not only to earn income but to make capital gain, as well. In such a case they consider the **holding – period return**, i.e. when possible price rise is incorporated in the expected return, as the following formula:

* R*

**H = [D + (P1 – P0)] / P0**

*(2.1.b)** *

*D: Dividend or coupon payment over the period*

*P1**: The price at the end of the period*

*P**0**: The current price.*

Although theoretically the above equation is of good use, in practice there are two disadvantages. First, we are not quite sure about the accuracy of the P1, and secondly, D can not always be regarded a ‘guaranteed’ and ‘safe’ income payment. As a result, what we are actually doing is to forecast the P1 (the price at the end of the period), and the *R*H, as well. Consequently, we undertake **risk** whenever we are trying to forecast the expected return.

#### 2.1.2 Risk

As stated earlier, risk is the possibility of having a final (actual) return that differs from the return that was expected (our initial estimation). In other words, it is the uncertainty that is related to the variability of returns.

There are **risk free** investments, e.g. a government bond that guarantees its holder the X amount after Z days. On the contrary, due to the variability of their returns, there are **very risky** investments, e.g. a holder of a company’s stocks.

**2.2 Risk Measurement**

In order to decide under uncertain conditions, e.g. investing in the stock market, it is helpful to measure the risk that is embodied in our decision. In addition to its **range**[1] and to **probability**[2], we have to apply statistical analysis for quantitative measurements of the risk, or, in other words, of the likely variability of its returns. More specifically, we can utilize the **standard deviation**[3] – *an indicator (equation 2.2.a) that measures the dispersion around the expected value [4] (equation 2.2.b)*, and the

**coefficient of variation**–

*an indicator that measures the relative dispersion or relative risk, useful in comparing the risk with different (2.2.c) expected values.*

k*j *: return for the *j*th outcome

Pr*j *: Probability of occurrence of the *j*th outcome

n: number of outcomes considered

**Finally**, it will be to the benefit of the prospective investor to choose the lowest risk asset, comparing the coefficient of variation rather than the standard deviation. This is due to the fact that the coefficient of variation also considers the standard deviation (σk) and the expected value (k), as well. For example, the asset A, with CV = 0.75, σk = 4.5% and k = 6% although has a lower σk has a higher CV compared to asset B, with CV = 0.5, σk = 5% and k = 10%, which, due to its lower CV (0.5 vs 0.75), should be preferred.

[1] The range is calculated by subtracting the pessimistic outcome from the optimistic outcome.

[2] The probability is the change or likelihood that a given outcome will happen.

[3] Rule of thump: A higher standard deviation means a higher risk and a higher possible return.

[4] The expected value is the most likely return on a given asset.