Investment Definition
An investment in shares is a contribution in a business acquiring securities or directly from an enterprise to obtain additional profit or influence the affairs of an enterprise or company. Investments differ depending on the type of the end resource of the investment, such as securities, start-ups, or other types of assets. While investments are aimed at making an investor a profit, they are not a guaranteed way to get it. Investing in different sources, taking into account their characteristics, provides a different level of return or its absence (Harmeyer, 2001). For financial literacy, it is not enough to understand investments. It is essential to save money correctly and competently in order to be able to invest it.
The Role of Math in Investing
Assessing Risks
The benefit of mathematics lies in the fact that it provides convenient tools for solving problems. First, mathematics is important in investing because it helps assess risks. This can be seen in an example of a critical mathematical calculation of an investment, which may be systematic and idiosyncratic risks.
Idiosyncratic risks are those that are linked to stocks. The airline’s plane may crash, and the corporation’s factory may burn down, leading to a stock fall. As discussed above, a company’s stock will provide investors with an additional expected return to the extent that the airline’s stock is linked to the market and the general economy. If diversification does not help, this means that another type of risk is taking place – systematic (Groves, 2022). The risk that the tangent market portfolio will fall in price falls into this category.
Calculating the Market Risk Premium
Secondly, the importance of mathematics in investments is due to the ability to calculate the market risk premium with its help. The expected excess return of each asset or portfolio of assets above the risk-free interest rate is related to the market’s expected excess return through the coefficient β. For the practical application of CAPM, a reasonably broad stock index, such as the S&P 500 or MSCI World (Jiang, 2022), is usually chosen.
A stock portfolio with the same weight as the index is solemnly declared a proxy for a hypothetical market portfolio of risky assets. The risk premium is the extra return assets can generate over risk-free bonds. The premium depends on the nature of investment risks – a system of factors that can affect asset quotes and the situation on the stock market as a whole.
Applying the Sharpe Ratio
Thirdly, mathematics provides an important tool, the Sharpe ratio. This calculation segment divides the return above the risk-free rate by the risk, measured as a standard deviation (Wang et al., 2022). The higher the return and the lower the standard deviation, the better the balance of risk and return. The Sharpe ratio measures risk by standard deviation. The sample standard deviation formula equally accounts for unexpected deviations from the average return.
Example of the Importance of Math in Investing
Mathematics is fundamental because, in the case of calculating systematic and idiosyncratic risks, it allows investors to avoid losing their capital. Thus, formulas and calculations are the most important part of an investor’s work. Every aspect of mathematics is somehow aimed at increasing money when investing.
This can be illustrated using the Capital Asset Pricing Model (CAPM). The investment situation can be modeled in such a way that an investor has invested a certain share of his capital in the market portfolio and a second share in a risk-free asset. The expected excess return above the risk-free interest rate is directly proportional to the share of investments in the first market portfolio and its expected excess return. This is called the market portfolio, which is also called the market risk premium. When the invested amount reaches a certain figure, there is no need to analyze the financial statement, as the result becomes obvious (CFI Team, 2022). If next year is good and the market return is higher than the risk-free rate, the stock will generate more excess returns.
References
CFI Team. (2022). Capital Asset Pricing Model (CAPM). CFI. Web.
Groves, J. (2022). Risk vs. Volatility: What’s The Difference? Forbes. Web.
Harmeyer, K. (2001). Consumer Mathematics. Ags Pub.
Jiang, B. (2022). Volatility Effect. In Investment Strategies. Palgrave Macmillan, Cham. Web.
Wang, C. D., Chen, Z., Lian, Y., & Chen, M. (2022). Asset selection based on high frequency Sharpe ratio. Journal of Econometrics, 227(1), 168-188. Web.