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 (PDFIS), 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:


                        RH = [D + (P1 – P0)] / P0                                                                                                  (2.1.b)


D: Dividend or coupon payment over the period

P1: The price at the end of the period

P0: 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 RH, 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 variationan indicator that measures the relative dispersion or relative risk, useful in comparing the risk with different (2.2.c) expected values.

kj : return for the  jth outcome

Prj : Probability of occurrence of the jth 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.


Risk Management – Part A

Manolis Anastopoulos @ University of Leicester - Risk Management


It is a historically known fact that people instead of keeping their cash with a zero return, decided to lend their surplus funds from the moment that the borrowers were willing to offer them a return.

On the other hand, as we know from economics, in order to acquire something we have to pay the price of having less of something else. As stated in their book, (Parking & King 1992), ‘More corn can be grown only by paying the price of having less cloth’.

In other words, it is a prerequisite for the surplus units to loose certainty, i.e. to accept risk, in order to gain return. This is the meaning of ‘risk’, the probability of ‘losing money’.

However, it can be generally argued that the majority of investors like to avoid risk whenever possible; they are risk–averse. As stated in their book, (Gitman & Madura 2001), ‘Given two choices with similar expected returns, they (the investors) prefer the less risky one.’  Consequently, investors are willing to accept increased risk only if they will be compensated with an increased rate of return. In other words, there is always a positive link between any claim’s uncertainty (risk) attached to its future performance and the required rate of return.


Portfolio Theory - Modern Portfolio Theory (MPT)

Investors, before the 1950s - based on the aforementioned ‘rules’ - used to focus on assessing the risk of individual securities in order to construct their portfolios[1]. For example, if an investor considers that the bank’s XX stocks were offering a satisfactory risk – reward characteristics, then he might construct his portfolio entirely of the stocks in question.

Later, in 1952, Harry Markowitz with his paper ‘Portfolio Selection’[2] introduced what is known as Modern Portfolio Theory.  Based on the concept of ‘diversification’ of the risk and ‘correlation’ of securities, he proposed that investors should select portfolios taking into consideration the portfolio’s overall risk – reward characteristics. More specifically, he argued that instead of tracing the risk’s level of individual securities, investors should measure their portfolios’ overall risk.


[1] Portfolios are usually constructed by different assets, such as: stocks, mutual funds, bonds and cash.

[2] Markowitz’s paper ‘Portfolio Selection’ published in 1952 by ‘The Journal of Finance.’