Finance for Managers

a) Calculation of rates of return and standard deviation

(1) Historical monthly rates of return for the market index

The rate of return can be calculated using following formula:


  • P0 = stock price in the beginning
  • P1 = stock price at ending

For calculating the historical monthly rates of return for the market index, the formula as mentioned above will be used as follws:-

  • Jan-20: (75179/71814) – 1 = 4.69%
  • Feb-20: (71814/69106) – 1 = -8.08%
  • Mar-20: (69106/54634) – 1 = -20.94%
  • Apr-20: (54634/59847) – 1 = 9.54%
  • May-20: (59847/62826) – 1 = 5.04%

The rate of return (ROR) is a presentation of gain (or loss) against the initial investment cost over a specific period of time. It is generally represented in the form of percentage and indicates a positive value when the security generate profits and. However if ROR comes out to be a negative figure, then it indicates that the investor has incurred some loss on its invested capital.

(2) Historical average rate of return and standard deviation of returns

Average Return: it is an indication of the average past performance of a security, portfolio or index.

The average returns for the mentioned securities (NCK and RC), portfolio and index is calculated below:

  • Index: -9.75% / 5 = -1.95
  • NCX: 8.42% / 5 = 1.68%
  • RC: 44.00% / 5 = 8.80%
  • Portfolio: 29.77% / 5 = 5.95%

Standard Deviation: represented by 'σ' is a measure of the levels of variation or dispersion of a data set as compared to its average (or mean). SD also helps analysts and investors in understanding how much the data set are reliable.

A smaller SD is preferred by large crowd of investor which indicates smaller risks. Basically small SD indicates that periodical data points are closely lying to the average value, indicating lower risk and higher reliability. At the opposite side, a larger SD indicates larger overall risks and that the data points are spreading far from the average value and thus there will be low reliability.

Calculation: SD is calculated by taking the square root of the variance value. Variance can be calculated as the sum of square of the difference between the observation points against the mean value.


On the basis of the above formula, the standard deviation of the index, NCK, reference company and portfolio has been calculated as follows.




Reference Company
































Standard Deviation





b) Calculate expected returns and portfolio beta

(1) Estimation of the expected return using CAPM

CAPM (The Capital Asset Pricing Model) is a very popular method to model and determine the expected rate of return. It establishes a relation between the expected rate of return for a particular security and the beta of the security. However, the method is primarily used to model equity stocks and similar securities, but due to its flexibility, it is widely utilized to price and value various other securities also and to calculate their expected returns.

Calculation: The CAPM method determines the expected rate of return by adding the risk free rate with the product of beta (of security) and risk premium.


  • ER = expected rate of return
  • Rf = risk-free rate
  • β = Beta (systematic risk identifier)
  • Rp = Risk premium

To calculate the expected rate of return for the securities in the case study, the following information has been provided:

  • Beta of NCK= 1.09
  • Rf = 0.883%
  • Beta of RC = -0.4
  • Rp = 6%

Calculation of expected rate of return:

NCX: Rf + βNCX * Rp

ð 0.88 + 1.09 * 6%

ð 7.42%

RC: Rf + βRC * Rp

ð 0.88 + -0.4 * 6%

ð -1.52%

b) Calculate the portfolio expected return and beta


Individual Securities



Expected Return


Expected Return













Reference Company












The expected return and beta of portfolio is:

(1) Expected return = 3.02% and

(2) Beta = 0.356.

c) Discussion of the calculated risk and return measures

The most important goal of an investor is to earn higher returns with lower risks and therefore determination of rate of returns has utmost importance because it checks how much returns a security is generating over different periods and thus measures the financial performance of that security.

However, the rates of return are not able to provide full information and it is required to compare the security returns with an index or some peer company. Hence, index returns have also been calculated in the analysis of the performance of stock of NCK and that of Reference Company. The following graph is presenting the rates of returns of NCK and index at different points of time:-

NCK tends to move in opposite direction as compared to the index in the periods of Jan 20 and Feb 20. This trend indicates that the correlation between the returns of index and the stock returns of NCK is negative. However the scenario changed from the month of March, where the stock return comes in positive correlation with the index returns. The index returns were -21% in March and in the months of April and May it became 9.5% and 5% respectively.

Similarly, returns of NCK remains -53% in March (indicating heavy risk) and became positive in the months of April and May to 38% and 20% respectively. It is also interesting to note in the last three months the returns of NCK are positively correlated to the index returns, but are moving with very high volatility as compared to the index returns. Also ADH on one hand highly underperformed the market in March, it outperformed the index at substantially higher levels and the returns jumped to 76% and 18% in the next months.

Risk and return are the two very important concepts of security analysis. It states that investors are risk averse and wants to get compensated for exposing to higher levels of risks. That means, with high levels of risk comes high potential returns, and vice versa.

The theory of diversification states that don’t put all your eggs in one basket, which means that don’t invest all your capital in a single security rather make a portfolio of various securities to reduce the overall risk. This is known as systematic allocation of the capital.

As per the previous discussions, NCK outperformed the index in the last two months and underperformed in the beginning couple of months. Also, the associated risks of

NCK of 34% is very high than that of index of12.5%. That is why, NCK witness heavy loss in the month of March and heavy profits in later months against index. On the other hand, the reference company was not able to outperform the index (except the month of February and March), also it has higher standard deviation than index.

Comparing NCK with RC, it can be seen that RC is outperforming NCK with average returns, but excluding the returns of March, the average returns of NCK becomes 15% and just 1% for RC. That means the month of March is an outlier and NCK can be considered to be a better performer as compared to RC, but is also exposed to higher risk.

Based on the above analysis, it is recommended to create a portfolio of NCK and RC in the ratio of 40% to 60%. With the portfolio, the overall exposure of risks falls to satisfactory levels of 5.72%, while generating a rate of return of 6%. Excluding the month of March, the portfolio risk will be 6.31% and portfolio returns will be 6.72%.

Investors want to get compensated for both the time value of money and the risk. The factor of time value of money is accounted under the risk-free rate (Rf) of CAPM. The other components including risk premium and beta of the CAPM method determines the additional risk factor than an investor is getting the exposure of. Beta is the measure of systematic (or non diversifiable risk) and market risk premium is the expected rate of return from the market above the risk-free rate of return.

The expected return calculated using CAPM is the returns expected by the investors in the future periods; the expected return is basically the cost to the company that it is expecting to pay to its investors or shareholders. NCK has higher expected return of 7.42%. On the other hand, RC has negative returns due to negative beta, which is a very rare situation, shows an inverse relation with the market (index). The results suggests that in future the market along with the stocks of NCK are going to perform much better, while the stocks of reference company might witness negative returns in the near future periods.

Reference for Financial Management

1. Almeida, G.L., Petralia, G., Ferro, M., Ribas, C.A.P.M., Detti, S., Jereczek-Fossa, B.A., Tagliabue, E., Matei, D.V., Coman, I. and De Cobelli, O., 2016. Role of multi-parametric magnetic resonance image and PIRADS score in patients with prostate cancer eligible for active surveillance according PRIAS criteria. Urologia internationalis, 96(4), pp.459-469.

2. Beyhaghi, M. and Ehsani, S., 2017. The cross-section of expected returns in the secondary corporate loan market. The Review of Asset Pricing Studies, 7(2), pp.243-277.

3. Eschenbach, T.G. and Lewis, N.A., 2019. Risk, standard deviation, and expected value: when should an individual start social security?. The Engineering Economist, 64(1), pp.24-39.

4. Singhal, S., Choudhary, S. and Biswal, P.C., 2019. Return and volatility linkages among International crude oil price, gold price, exchange rate and stock markets: Evidence from Mexico. Resources Policy, 60, pp.255-261.

5. Sukono, D.S., Najmia, M., Lesmana, E., Napitupulu, H., Putra, A.S. and Supian, S., 2018. Analysis of stock investment selection based on CAPM using covariance and genetic algorithm approach. In IOP Conference Series: Materials Science and Engineering (Vol. 332, p. 012046).

6. World Government Bonds. 2020. Australia Government Bonds - Yields Curve.

7. Kapoor, R., Gupta, R., Jha, S. and Kumar, R., 2018. Boosting performance of power quality event identification with KL Divergence measure and standard deviation. Measurement, 126, pp.134-142.

8. Sim, T. and Wright, R.H., 2017. Stock valuation using the dividend discount model: An internal rate of return Approach. In Growing Presence of Real Options in Global Financial Markets. Emerald Publishing Limited.

9. Sukono, D.S., Najmia, M., Lesmana, E., Napitupulu, H., Putra, A.S. and Supian, S., 2018. Analysis of stock investment selection based on CAPM using covariance and genetic algorithm approach. In IOP Conference Series: Materials Science and Engineering (Vol. 332, p. 012046).

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Accounting and Finance Assignment Help

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