This document discusses concepts related to risk and return analysis in finance. It defines key terms like return, expected return, risk measures including beta, standard deviation, and alpha. It also categorizes different types of risk and explores the relationship between risk and return. Methods for computing rates of return from market data and calculating variance and standard deviation of returns are presented.

1. MBEYA UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT : MECHANICAL AND INDUSTRIAL
EMGINEERING.
PROGRAM : BARCHELOR IN MECHANICAL
ENGINEERING
TASK : GROUP 1. ASSIGNMENT.
MODULE NAME : ENGINEERING ECONOMICS
MODULE CODE : ME. 8311
LEVEL : UQF 8 THIRD YEAR,
MODULE MASTER: MR. MWANGOMO

2. Question:
• Risk and Return analysis; Define and measure return and expected
returns; Define, measure and explain different types of risk; Describe
the relationship between risk and return; Use market information to
compute rate of return, variances and standard deviation of returns;
Define and measure risk and expected return in a portfolio context;
Annalise the power of diversification in achieving superior return for a
given level of risk or minimum risk for a given level of expected
return and Determine optimal portfolio weights and Capital Asset
Pricing Model (CAPM)

3. Risk and Return analysis
Return
• This is the total gain or loss experienced on an investment over a given
period of time; calculated by dividing the asset’s cash distributions
during the period, plus change in value, by its beginning-of-period
investment value.
• It is commonly measured as cash distributions during the period plus
the change in value, expressed as a percentage of the beginning-of-
period investment value.

6. Example

7. Expected Return
An investor's expected return is the total amount of money they expect to gain or
lose on a particular investment or portfolio. Investors commonly use the expected
return to help them make key decisions on whether to invest in new project or
continue to hold on to their existing investments.
The expected return is generally based on historical returns. As such, it doesn't
indicate the potential for future performance and shouldn't be used as the only
decision-making tool. This metric can, however, give investors a reasonable
expectation of what they may expect in the short- and long-run.
• Expected Portfolio Return = (Asset 1 Weight x Expected Return) +
(Asset 2 Weight x Expected Return)

8. Risk measures
• Beta (Measurement of systematic risk)

9. BETA CONT …

10. Standard Deviation
• Standard deviation is a method of measuring data dispersion in regards
to the mean value of the dataset and provides a measurement regarding
an investment’s volatility.
• As it relates to investments, the standard deviation measures how
much return on investment is deviating from the expected normal or
average returns.

11. Alpha
• Alpha measures risk relative to the market or a selected benchmark
index. For example, if the S&P 500 has been deemed the benchmark
for a particular fund, the activity of the fund would be compared to
that experienced by the selected index. If the fund outperforms the
benchmark, it is said to have a positive alpha. If the fund falls below
the performance of the benchmark, it is considered to have a negative
alpha.

12. Types of Risk
• The following are types of risks on different basis.

13. I. On the basis of occurrence; pure and speculative
risk
• Pure risk
This exists when there is uncertainty as to whether loss will occur or
not. No possibility of gaining is presented by pure risk.
• speculative risk exists when there is uncertainty about an even that
could produce either profit or loss. This risk offers the possibility of
gain or loss.
II. On the basis of flexibility; static and dynamic risk.
• Static risk. This remain indifferent in changing economic
environment.
• Dynamic risk. This resulting from change in the economics e.g.
Change in inflation rate, consumer tastes, income level

14. III. On the basis of measurement; financial and
non-financial risk.
• Financial risk. Refers to uncertainty which can be measured in terms of
money.
• Non-financial risk. Refers to uncertainty which can’t be measured in terms
of money.
IV. On the basis of coverage; fundamental and particular risk
• Fundamental risks. Are those risks which tend to affect large section of
society, entire economic, large number of persons rather than individuals.
• Particular risk. This is associated with an industry, firm, or an investment
option, therefore its measurement and both play vital role in determining
rate of return.

15. V. On the basis of behavior; subjective and
objective risk.
• Subjective risk. Refers to the mental state of an individual whose
experiences doubt or worry as to the outcome of the given event.
• Subjective risk α conservative behavior.
• Objective risk. This is more precise, observable and measurable. In
general objective risk the possible variation of actual from expected
experience.
• Objective risk α
𝟏
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒆𝒙𝒑𝒐𝒔𝒖𝒓𝒆

16. VI. On the basis of diversification; diversified
(unsystematic) and non-diversified (systematic)
risk.
• Diversified (unsystematic) risk. This is very much inherent in the system
and cannot be separated from the system (an organization, industry, class of
securities). OR
• Unsystematic risk represents the asset-specific uncertainties that can affect
the performance of an investment.
• Non-diversified (systematic) risk. This is the level of risk which can be
reduced or managed by diversifying investment. Such risks are not rooted in
the system. OR
• Systematic risk is the market uncertainty of an investment, meaning that it
represents external factors that impact all (or many) companies in an
industry or group.

18. Relationship between risk and return.
You Can't Have One Without the Other
• Understanding the relationship between risk and return is essential to
understanding why people make some of the investment decisions
they do.
• First is the principle that risk and return are directly related. The
greater the risk that an investment may lose money, the greater its
potential for providing a substantial return. By the same token, the
smaller the risk an investment poses, the smaller the potential return it
will provide.

19. Computing rate of return using market
information.
Rate of return is the measure of an investment's performance over a period of
time, expressed as a percentage of its initial cost. A positive return reflects a
gain in the investment's value, while a negative return reflects a loss in value.
A rate of return calculates the percentage change in value for any investment,
regardless of whether it continues to be held, or was sold.
Rate of return can be used to measure the monetary appreciation of any asset,
including stocks, bonds, mutual funds, real estate, collectibles, and more.
Calculating a rate of return requires two inputs:
• The investment purchase amount
• The current or ending value of the investment for the period being measured

20. A simple rate of return is calculated by subtracting the initial value of the
investment from its current value, and then dividing it by the initial value. To
report it as a %, the result is multiplied by 100.
Rate of Return % = [(Current Value – Initial Value) / Initial Value] x 100
For example, if a share price was initially $100 and then increased to a
current value of $130, the rate of return would be 30%.
[($130 - $100) / $100] x 100 = 30%
Rate of returns can certainly be negative as well, if the asset has lost value.
For the above example, if the share price had declined to $70, it would reflect
a -30% rate of return.

21. Variances and standard deviation of returns
Variance is a metric that is needed to estimate the squared deviation of any
random variable from the mean value. In the portfolio theory, the variance of
return is called the measure of risk inherent in a singular or in an asset of
portfolios.
In general, the higher the value of variance, the bigger is the squared
deviation of return of the given portfolio from the expected rate. The higher
values show a larger risk, and low values indicate a lower inherent risk.
There are two different approaches to calculate the variance of returns −
1. Probability Approach
2. Historical Return Approach

22. Probability Approach
The probability approach for determining variance is used when the complete
set of possible outcomes is available. This means the probability distribution
of the asset or portfolio is known in advance.
The equation of variance formula in the Probability approach can be written
as follows −
σ2=∑i=1n(ri−ERR)2×piσ2=∑i=1n(𝑟𝑖−ERR)2×p𝑖
Where,
• 𝑟𝑖 is the rate of return achieved at ith outcome,
• ERR is the expected rate of return,
• 𝑝𝑖 is the probability of ith outcome,
• n is the number of possible outcomes

23. Historical Return Approach
• The historical return approach is more generally used in investing and
finance. Using finite data set of the history of the investment in an asset or a
portfolio, the return is calculated with assumptions that each possible
outcome has the same probability. Thus, the variance of return on a single
asset or portfolio is measured as −
σ2=∑ni=1(ri−ERR)2Nσ2=∑i=1n(𝑟𝑖−ERR)2N
where, N is the size of the entire population.
• The above formula considers the idea that a dataset represents the entire
population, but in numerous practical situations, a sample of the given
population is used instead of the entire population which may be very large.
Therefore, a sample variance is an estimation of the variance of the entire
population −
σ2s=∑ni=1(ri−ERRs)2N−1σs2=∑i=1n(𝑟𝑖−ERRs)2N−1
where ERRS is the expected rate of return of a sample or sample mean, and N
is the size of the sample.

24. Standard Deviation
The standard deviation of a portfolio measures how much the
investment returns deviate from the mean of the probability distribution
of investments. Put simply, it tells investors how much the investment
will deviate from its expected return. As such, investors can use this
metric to help determine an investment or portfolio's annual return by
considering its historical volatility.
The standard deviation is calculated as follows:

27. Expected Return
An investor's expected return is the total amount of money they expect
to gain or lose on a particular investment or portfolio. Investors
commonly use the expected return to help them make key decisions on
whether to invest in new vehicles or continue to hold on to their existing
investments.
The expected return is generally based on historical returns. As such, it
doesn't indicate the potential for future performance and shouldn't be
used as the only decision-making tool. This metric can, however, give
investors a reasonable expectation of what they may expect in the short-
and long-run
Expected Portfolio Return = (Asset 1 Weight x Expected Return) +
(Asset 2 Weight x Expected Return)

28. Now let's use a hypothetical example to show how to apply the formula.
The table below shows a portfolio with three different investments, each
with different weightings and expected returns
Asset Weight Expected Return
A 35% 6%
B 25% 7%
C 40% 10%
The expected return of the overall portfolio would be 7.85%. We arrive at this result by using the formula
above:
(35% x 6%) + (25% x 7%) + (40% x 10%) = 7.85%
An investor uses an expected return to forecast, and standard deviation to discover what is performing well and
what is not.

29. Analyses of power of diversification in achieving superior return for a given
level of risk or minimum risk for a given level of expected return.
Diversification is a risk management strategy that mixes a wide variety of investments within a
portfolio in an attempt to reduce portfolio risk.. A diversified portfolio contains a mix of distinct asset
types and investment vehicles in an attempt at limiting exposure to any single asset or risk.
Note
• Diversification is most often done by investing in different asset classes such as stocks, bonds, real
estate, or cryptocurrency.
• Diversification can also be achieved by buying investments in different countries, industries, sizes
of companies, or term lengths for income-generating investments.
• Diversification is most often measured by analyzing the correlation coefficient of pairs of assets.
• Investors can diversify on their own by investing in select investments or can hold diversified
funds that diversify on their own.
Diversification strives to smooth out unsystematic risk events in a portfolio, so the positive
performance of some investments neutralizes the negative performance of others. The benefits of
diversification hold only if the securities in the portfolio are not perfectly correlated—that is, they
respond differently, often in opposing ways, to market influences

30. The 4 primary components of a diversified portfolio
Domestic stocks
• Stocks represent the most aggressive portion of your portfolio and provide the opportunity for
higher growth over the long term. However, this greater potential for growth carries a greater risk,
particularly in the short term. Because stocks are generally more volatile than other types of assets,
your investment in a stock could be worth less if and when you decide to sell it.
Bonds
• Most bonds provide regular interest income and are generally considered to be less volatile than
stocks. They can also act as a cushion against the unpredictable ups and downs of the stock market,
as they often behave differently than stocks. Investors who are more focused on safety than growth
often favor US Treasury or other high-quality bonds, while reducing their exposure to stocks.
These investors may have to accept lower long-term returns, as many bonds especially high-quality
issues, generally don't offer returns as high as stocks over the long term. However, note that some
fixed income investments, like high-yield bonds and certain international bonds, can offer much
higher yields, albeit with more risk.

31. Short-term investments
• These include money market funds and short-term CDs (certificates of deposit). Money
market funds are conservative investments that offer stability and easy access to your
money, ideal for those looking to preserve principal. In exchange for that level of safety,
money market funds usually provide lower returns than bond funds or individual bonds.
While money market funds are considered safer and more conservative, however, they are
not insured or guaranteed by the Federal Deposit Insurance Corporation (FDIC) the way
many CDs are. When you invest in CDs though, you may sacrifice the liquidity generally
offered by money market funds
International stocks
• Stocks issued by non-US companies often perform differently than their US counterparts,
providing exposure to opportunities not offered by US securities. If you're searching for
investments that offer both higher potential returns and higher risk, you may want to
consider adding some foreign stocks to your portfolio.

32. Capital Asset Pricing Model (CAPM)
• The Capital Asset Pricing Model (CAPM) describes the relationship
between systematic risk, or the general perils of investing, and expected
return for assets, particularly stocks. It is a finance model that establishes a
linear relationship between the required return on an investment and risk.
The model is based on the relationship between an asset's beta, the risk-free
rate (typically the Treasury bill rate), and the equity risk premium, or the
expected return on the market minus the risk-free rate.
• CAPM evolved as a way to measure this systematic risk. It is widely used
throughout finance for pricing risky securities and generating expected
returns for assets, given the risk of those assets and cost of capital.

33. Reference
1. Acharya, Nabraj, "Risk and Return analysis in common stock investment of some listed
companies of Nepal", An Unpublished MBS thesis, Lumbini Banijya Campus, Butwal, (2004)
2. Gitman, J. Lawrence, Principle of managerial finance, Third Edition Wright, stat University,
Happer and Row publisher, New york, (1988).
3. Joshi, Roopak, "Investors' problem on choice of optimum portfolio of stocks in Nepal. Stock
Exchange Ltd", An Unpublished MBS Thesis, Shanker Dev Campus, Kathmandu, (2002).
4. Mechael, J, Breman, and H, Henery "Internal Portfolio flows", Journal of finance, (1997).
5. Panthi Ramu, "Analysis of Risk and Return of common stock investment of commercial banks
of Nepal" An Unpublished MBS thesis, Lumbini Banijya Campus, Butwal, (2004).
6. Weston, J.F and E.F, Brigham, Essential of Managerial Finance ,8th edition Chicago Willam, F
Sharp" Capital Assets Price; A theory of market equilibrium under conditions of risk" Journal of
finance, September (1964).

34. Group members
S/N. NAME REG. NO. CA NO. SIGNATURE
1
STEVEN E. JOHN 20100134010001
2
MARIA Y. MWALUFYAGILA 20100134010141 CA/BME/22/12675
3
DONATUS S. PHABIANO 20100134010087 CA/BME/22/12693
4
KIJA N. MALEGI 20100134010140 CA/BME/22/12660
5
SHILINDE K. NICHOLAUS 20100134010097 CA/BME/22/12687
6
MAGEME P. MAGEME 20100134010050 CA/BME/22/12655
7
MAGINA M. MSUKA 20100134010150 CA/BME/22/12672
8
LOPUKENYA L. NGETUYA 20100134010064
9
REVOCATUS M. ELIAS 20100134010075
10
MUSSAALLY KITUMBIKA 20100134010083 CA/BME/22/12649
11
BAHATI K. KIIZA 20100134010139 CA/BME/22/12646
12
THOBIAS R. MINGARE 20100134010079
13
CHARLES M. KAPAGALA 20100134010060 CA/BME/22/12642
14
JACOB M. JOSEPHAT 20100134010042
15
BARNABA W. DIONIZ 20100134010148 CA/BME/22/12629
16
VICTOR NAFTAL 20100134010131
17
IGNAS J. MKWIZU 20100134010010 CA/BME/22/12669