Mathematical Finance

UNIT VII

Mathematics of Return and Risk

1.   Measuring Return and Risk

2. The Capital Asset Pricing Model

Unit VII Summary

List of Formulas

Exercises for Unit VII

1	Measuring Return and Risk

Financial securities such as stocks and bonds, as well as other investment assets, have to be evaluated to determine how good an investment they may offer. Such a process of valuation presents the opportunity to link and assess two of the most significant determinants of the security share price: risk and return, whose assessment is the core of all major financial decisions. Risk, in its most fundamental meaning, refers to the chance that an undesirable event will occur. In a financial sense, it is defined as the chance to incur a financial loss. When an asset or an investment opportunity is dubbed as “risky,” it would be thought to have a stronger chance of bringing a financial loss. It would refer implicitly to the variability of the returns of that asset. Conversely, the certainty of the return, such as the guaranteed return on a government bond, would refer to a case of no risk. We can say further that the investment risk refers to the probability of having low or negative returns on invested assets, such that the higher the probability of getting a low or negative return on an asset, the riskier that investment would be.

The return on an investment asset is defined by the change in value, in addition to any cash distribution, all expressed as a percentage of the asset original ...