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Risk, Return, and Capital Asset Pricing Model Assignment Sample


The CEO of SysConsult International commissioned this essay. Analysis of potential investments in Logical IT and Safeworth Grocery is the goal. The research of finance assignment makes the assumption that a one-year Treasury note will earn 5% over the following year, with Logical IT's beta being 1.70 and Safeworth Grocery's beta being 0.60. Table 1 below contains an examination of potential return rates for the two businesses under various economic scenarios.

Relationship between Risk and Rate of Return

General Rule

As a general rule, more risks are linked to greater potential rewards, whereas greater safety is linked to greater potential losses. A straightforward and common sense principle of companies seeking to acquire capital governs this connection. It is best to describe the situation by presuming that there is no such link. In this universe, regardless of volatility, all investments would yield the same rate of return. Therefore, there wouldn't be any incentives for investors to fund risky businesses or projects. In other words, only a select few businesses would be able to access the money from possible investors, as people would not want to take the chance of their money disappearing for no apparent reason.

In the real world, businesses have the opportunity to raise more money by providing investors with greater returns. Companies can either guarantee investors a portion of their income through dividend payments, or they can show that they will grow quickly, allowing investors to sell their shares at a profit. Potential investors have a cause to participate in businesses with high performance volatility thanks to incentives like these. Investors typically base their judgements on a comparison of potential returns and risks, choosing the market's optimum ratio. Investors are also influenced by their own level of risk tolerance, as some people may be unable to take a large risk of financial loss, regardless of how lucrative an investment could be.

Not a Direct Relationship

It should be noted that risk and return do not directly correlate. Bigger risks entail higher potential profits, where "potential" is the essential concept. A person must be willing to embrace the potential that they could lose some or all of the money they invest if they wish to fast expand their wealth. Two concrete examples—trading in penny stocks and cryptocurrencies—can be used to demonstrate this. Bitcoin and other cryptocurrencies are frequently linked to great profits. Figure 1 shows that if an investor had bought in October 2020 and sold in December 2020, their investment would have more than doubled.

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

Although purchasing Bitcoins may seem appealing, due to the extreme volatility of the exchange rates, it is not necessarily a safe investment. If investors had chosen to invest at the start of June 2021, as shown in Figure 2 below, they may have lost more than 40% of their money. Investors may also be higher at risk of losing money due to government laws against cryptocurrencies, low transaction and keeping security, and other factors. Twelve nations, including China and Russia, have outlawed cryptocurrency, indicating that further nations may do the same. Due to all of these factors, investors must be willing to risk the possibility of substantial losses in exchange for the potential for big profits.

Penny stocks are another illustration of the connection because they are regarded as high-risk investments because of the extreme share price volatility. Outside of the major stock exchanges, a small group of investors trade these equities at extremely low rates. As a result, if a substantial investor decides to buy shares, the stock price will increase significantly, giving other investors the chance to sell the stock at a premium. But these investments are frequently non-liquid, suggesting that nobody might desire to buy these equities. Additionally, the stock prices would decrease dramatically if a big investor decides to sell shares, which will result in losses.

Calculating the Expected Rate of Return

Definition and Formula

The anticipated rate of return is the value at which investors can expect a given probability distribution of probable returns. In other words, it is the result of adding the probability of all conceivable outcomes together. Given the probability distribution of outcomes, it may be seen as the typical return rate an investor should anticipate from an investment. An investor can determine if a stock is performing well or poorly using the expected rate of return as a benchmark. The expected rate of return is calculated using the following formula:

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


According to the estimates, Safe worth Grocery has the lowest predicted rate of return, while Logical IT has the best.

Calculating Standard Deviation

Definition and Formula

A measure of variability called standard deviation shows how much the actual data may deviate from the expected value in standard units. To put it another way, the standard deviation is a metric that shows how volatile a stock is predicted to be over a specific time frame. The following is the standard deviation formula:


• Rt = observed return rate
• R = expected return rate


According to the estimates, Logical IT has the largest standard deviation, indicating that its stock is the most volatile.

Beta and CAPM

Beta vs Standard Deviation

Beta or the standard deviation are two ways to quantify volatility. The standard deviation, as it was discussed in Section 4, is a gauge of a stock's volatility over a specific time period. A stock's price fluctuation in relation to a benchmark is shown by the relative measure of volatility known as beta (for example, ASX200 index). The stock, for instance, will be 20% more volatile than the market if the beta is 1.2. This suggests that the stock should increase by 12% if the market increases by 10%. When predictions regarding the performance of the benchmark index are available, beta is helpful. Higher betas are recommended if the market is anticipated to rise, whereas lower betas are preferred in all other scenarios.

Since it helps to make decisions knowing the forecast for the benchmark, beta is a stronger indicator of risk in this situation for the common shares of the IT company and the supermarket company. According to the ASX200 forecast, there is only a 30% risk of a market recession and a 70% likelihood that the market would grow.

Using Beta for Calculations

The projected rate of return for the two companies under examination can be determined using the beta of the companies. The capital asset pricing model (CAPM) can be used to do that. The CAPM formula is as follows:


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

Section 1 of the essay provides the betas for Logical IT and Safeworth Groceries as well as the risk-free rate. Section 3.2 of the essay provides the expected rate of return for the ASX200.

Following are the calculations for the two companies under analysis' projected rates of return:

If the cash flows are the same, Logical IT will be valued more because of its larger beta.

Volatility of the Benchmark

It is also vital to take into account how the anticipated return rate will vary if the market becomes unstable. Higher betas indicate that the value will likewise be more variable than projected. For instance, if the projected rate of the ASX200 falls by 5% (to 6%), Logical IT's share price will move more dramatically than Safeworth Groceries'. Following are the calculations:

This indicates how closely tied to market performance the value of Logical IT's shares is.

Portfolio Creation

Portfolio Beta

Putting such a portfolio is essential for protecting investments from threats. Investors want to distribute their capital among a variety of funds, including bonds, shares of small businesses, shares of internationally renowned companies, and shares of well-established foreign corporations. By making investments in various businesses, investors frequently diversify their portfolios. A technique like this helps protect the investor from the potential that the industry won't do well at a certain point in time. When it comes to Logical IT and Safeworth Groceries, investment in the grocery chain provides protection from the market's turbulence and the IT industry's performance.

A portfolio's beta, which is a weighted average of the betas of all the companies in the portfolio, can be used to describe it after it has been constructed. Understanding a portfolio's predicted volatility during the specified period is made easier with the help of the portfolio beta. The following formula is used to determine the portfolio's beta:

Two potential two-share portfolios were taken into account for investment. The first choice is to put $70,000 in Safeworth Groceries and $30,000 in Logical IT. According to this, 30% of the portfolio will presumably be invested in the IT company, and 70% in the grocery company. When it comes to portfolio beta:

The CAPM model can be used to determine the portfolio's anticipated rate of return:

According to the analysis, this option has a little lower risk than the ASX200 index. When the market prediction is unfavorable or fraught with uncertainty, this kind of portfolio may prove advantageous.

Alternatively, you might put $70,00 into Logical IT and 30% into Safeworth Groceries. The predicted rate of return and portfolio beta in this instance will be as follows:

Comparing this type of portfolio to the market benchmark of 11%, larger predicted returns are connected. When the outlook for the market is favourable, a portfolio like this is the ideal choice.


When comparing the two choices listed above, I would choose the second one, in which the IT business receives 70% of the funds and the food company receives 30%. As stated in Section 1 of the current paper, there is only a 30% likelihood of a market recession, thus the projection for the ASX200 index is favourable. Investors may be more risk-tolerant when the market is predicted to grow, so somewhat larger beta values are favoured. By investing in the grocery company in the second scenario, any potential underperformance of Logical IT is compensated for. It is advisable to safeguard the investment from the risk of a recession even though diversifying the portfolio reduced the possible rate of return from 15.2% to 13.22%. The expected returns from Logical IT will dramatically decrease if the market goes into a recession, whereas the expected returns from the grocery store are predicted to be rather steady (see Section 5.3). Additionally, buying in Safeworth Grocery shields funds against Logical IT's underperformance and market volatility.

Although the aforementioned advise seems to be appropriate, the investor ultimately has the last say. The investor's individual risk tolerance should be used as a reference when making investments. The 30% probability of underperformance may be too high for some investors. The first selection from the two-share portfolio is preferred in this situation. This portfolio's beta is only somewhat lower than the market benchmark, which suggests that predicted returns will be roughly average. The investor will also continue to be safe from any potential market turbulence.

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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