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Risk, Return, and Capital Asset Pricing Model

Introduction

The present report was commissioned by the CEO of SysConsult International. The purpose of the report is to analyse the possibility of investment in Logical IT and Safeworth Grocery. The analysis assumes that a one-year Treasury note will have a rate of return of 5% over the next year, the beta for Logical IT as 1.70 and beta for Safeworth Grocery as 0.60. The analysis of possible return rates for the two companies in case of different situations in the economy is provided in Table 1 below.

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Table 1. Rate of return estimations

Economic Condition Probability Estimated rate of Return from Investment
Logical IT Safeword Grocery ASX 200
Recession 30% -20% 5% -4%
Normal 20% 15% 6% 11%
Expansion 35% 30% 8% 17%
Boom 15% 50% 10% 27%

Relationship between Risk and Rate of Return

General Rule

It is a general rule that higher risks are associated with higher potential returns, while lower risks are associated with lower potential returns. This relationship is guided by a simple and natural rule of entities wanting to attract capital. It is best to explain the situation going by assuming that no such relationship exists. In this world, all investments would have the same rate of return regardless of their volatility. Thus, there would be no incentives for the investors to invest in volatile companies or projects. In other words, there would be a few companies that would get all the money from the potential investors, and all other companies will not be able to get access to investors’ money, as people do not want to risk losing money for no evident reason.

In the real world, the companies have the chance to attract additional funds by offering higher returns on investments. Companies can either offer dividends as a guaranteed way of giving away some of the company’s income to the investors or demonstrate that the company will grow very fast, which will let the investors sell off their shares with profit. Such incentives provide potential investors with the reason to invest in companies with high volatility in their performance. Investors usually guide their decisions by comparing the possible returns with the possible risks and selecting the best ratio in the market. Additionally, investors are guided by personal risk tolerance, as people may want to reject any investments no matter how high the possible return rate, as they are unwilling to accept the high risk of losing money.

Not a Direct Relationship

It should be noticed, the relationship between risk and return is not direct. Accepting higher risks means seeking higher potential returns, where the word “potential” is the key. If a person wants to increase his or her wealth quickly, they need to accept the possibility that they will lose some or all the invested money. This can be illustrated in two vivid examples of trading with cryptocurrencies and penny stocks. Cryptocurrencies, such as Bitcoin are usually associated with high returns. Figure 1 demonstrates that an investor could have more than doubled the money if invested in October 2020 and sold in December 2020.

Bitcoin-USD exchange rates between October 2020 and December 2020
Figure 1. Bitcoin-USD exchange rates between October 2020 and December 2020(Yahoo Finance, 2021)

While investing in Bitcoins may appear attractive, it is not always safe to invest in it, as the exchange rates are associated with high volatility. Figure 2 below demonstrates that investors could have lost more than 40% of the money if they decided to invest at the beginning of June of 2021. Additionally, investors may face the chance of losing all the more due to low transaction and keeping security, no insurance, and government regulations against cryptocurrencies. There are 12 countries that banned cryptocurrencies, including Russia and China, which shows that other countries may follow. All of these matters mean that investors need to accept the possibility of losing much money for the chance of high returns.

Bitcoin-USD exchange rates in June 2021
Figure 2. Bitcoin-USD exchange rates in June 2021 (Yahoo Finance, 2021)

Another example of the relationship is penny stocks, which are considered high-risk investments due to the high volatility of share prices. These stocks are traded at very low prices with a limited number of investors outside the major stock exchanges. Thus, if a large investor decides to purchase shares, the price of the stock will grow significantly, which will provide other investors with the opportunity to sell the stock at a high price. However, such investments are often non-liquid, which implies that nobody may want to purchase these stocks. Additionally, if a large investor decides to sell shares, the stock prices will drop significantly, leading to losses.

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​Calculating the Expected Rate of Return

Definition and Formula

Expected rate of return is the expected value of the probability distribution of possible returns it can provide to investors. In other words, it is the sum of all the possible outcomes multiplied by their probabilities. It may be treated as an average return rate an investor should expect from an investment given the probability distribution of outcomes. The expected rate of return serves as a benchmark for an investor to assess if the stock is underperforming or overperforming. The formula for the expected rate of return is the following:

Formula

Where:

  • E(R) = Expected Rate of Return
  • Rn = Return Rate in case of n
  • Pn = Probability of n occurring

Calculations

Formula
Formula
Formula

The calculations demonstrate that Logical IT has the highest expected return rate, while Safeworth Grocery has the lowest expected rate of return.

Calculating Standard Deviation

Definition and Formula

Standard deviation is a measure of variability that demonstrates how much the actual values may differ from the expected value in standard units. In other words, the standard deviation is a measure that demonstrates how volatile is a stock expected to be during the given time period. The formula for standard deviation is the following:

Formula

Where:

  • Rt = observed return rate
  • = expected return rate

Calculations

Formula
Formula
Formula

The calculations demonstrate that Logical IT has the highest standard deviation, which demonstrates that it is the most volatile stock.

Beta and CAPM

Beta vs Standard Deviation

Volatility can be measured by standard deviation or beta. As it was mentioned in Section 4, the standard deviation is a measure of the volatility of a stock during a defined period. Beta is a comparative measure of volatility that demonstrates how much a stock price changes in comparison with a benchmark (for example, ASX200 index). For instance, if the beta is 1.2, the stock has 20% more volatility than the market. This implies that if the market grows by 10%, the stock is expected to grow by 12%. Beta is useful when projections about the performance of the benchmark index are available. If the market is expected to be rising, higher betas are preferable, while lower betas are preferred otherwise.

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In the present case, beta is a better measure of risk for the ordinary shares of the IT firm and the grocery firm, as it helps to make decisions knowing the forecast for the benchmark. The prognosis for ASX200 is available, and there is a 70% chance that the market will be growing and only a 30% chance of recession.

Using Beta for Calculations

The beta of the companies can be used to calculate the expected rate of return of the two companies under analysis. In order to do that, the capital asset pricing model (CAPM) can be used. The formula for CAPM is the following:

Formula

Where:

  • Rf = risk free rate (treasury note)
  • βi = company beta
  • E(Rm)= benchmark return rate (ASX200)

The betas for Logical IT and Safeworth Groceries and the risk-free rate are provided in Section 1 of the present report. The estimated rate of return for ASX200 is provided in Section 3.2 of the present report. The calculations for the expected rate of return for the two companies under analysis are provided below:

Formula
Formula

In the case of identical cash flows, Logical IT will be valued higher, as its beta is higher.

Volatility of the Benchmark

It is also crucial to consider how the expected return rate will change in case of market instability. Higher betas mean than the expected value will also be more volatile. For instance, if the expected rate of ASX200 decreases by 5% (to 6%), the percentage change in the share prices of Logical IT will be higher than that of Safeworth Groceries. The calculations are provided below:

Formula
Formula

This demonstrates that the value of Logical IT’s shares is highly dependable on the market performance.

Portfolio Creation

Portfolio Beta

Creating a portfolio is crucial for defending investments against risks. Investors prefer to allocate their money into different types of types of funds, such as shares of small companies, shares of well well-established companies abroad, and bonds. Investors often diversify their portfolios by investing in different industries. Such a strategy helps to defend the investor from the possibility of the sector not performing well during a particular time period. In the situation with Logical IT and Safeworth Groceries, investing in the groceries company helps to defend against the volatility of the market and performance of the IT sector.

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When a portfolio is created, it can be characterised by a portfolio beta, which is a weighted average of the betas of all the companies in the portfolio. The portfolio beta helps to understand how volatile a portfolio is expected to be during the defined period. The beta of the portfolio is calculated using the following formula:

Formula

Two possibilities of two-share portfolios were considered for investment. The first option is to invest $30,000 in Logical IT and $70,000 in Safeworth Groceries. This implies that 30% of the portfolio will be invested in the IT firm, and 70% will be invested in the grocery company. In this case, portfolio beta:

Formula

The expected rate of return for the portfolio can be calculated using the CAPM model:

Formula

The analysis demonstrates that this option is associated with a slightly lower risk than the ASX200 index. This type of portfolio can be useful when the forecast for the market is unfavourable or associated with a high degree of uncertainty.

Another option was to invest $70,000 in Logical IT and 30% in Safeworth Groceries. In this case, the portfolio beta and the expected rate of return will be the following:

Formula
Formula

This type of portfolio is associated with higher expected returns in comparison with the market benchmark of 11%. Such a portfolio is the best option when the forecast for the market is favourable.

Recommendations

When considering the two options provided above, I would favour the second one, when 70% of the funds are allocated to the IT company, and 30% of the money is placed in the grocery company. As mentioned in Section 1 of the present paper, the forecast for the ASX200 index is favourable, as there is only a 30% chance of market recession. When the market is expected to grow, slightly higher beta values are preferred, as investors can be more risk-tolerant. In the second option, the possibility of underperformance of Logical IT is offset by investment in the Grocery company. Even though diversifying the portfolio decreased the potential rate of return from 15.2% to 13.22%, it is best to protect the investment from the risk of recession. If the market experiences a recession, the expected returns from Logical IT will drop significantly, while the returns from the grocery company are expected to be relatively stable (see Section 5.3). Additionally, investing in Safeworth Grocery helps to protect the money from volatility in the IT market and underperformance of Logical IT.

While the recommendation provided above appears to be appropriate, the final decision is made by the investor. Investment decisions are to be guided by the personal risk tolerance of the investor. For some investors, the 30% chance of underperformance is too high. In this case, the first option of the two-share portfolio is preferred. The beta of this portfolio is only slightly below the market benchmark, which implies that the expected returns will be close to average. At the same time, the investor will stay protected from the possible volatility of the market.

Reference List

Orji, C. (2021). Bitcoin ban: These are the countries where crypto is restricted or illegal. EuroNews.

Yahoo Finance. (2021). Bitcoin USD (BTC-USD). 

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