WORKBOOK

INVESTMENT INSTOCK
MARKET(E)

RISK & RETURN

B.A.(H)ECONOMICS

SUBMITTED TO:
MS. MANSI KANOJIA
DATE OF SUBMISSION:
SUBMITTED BY: 25TH NOVEMBER 2024
KHUSHI JHA (ECO23042)
 GE Workbook
RISK AND RETURN
Risk and Return Trade off:
The risk-return trade-off refers to the principle that higher potential returns on investment usually
come with higher levels of risk. It is a fundamental concept in finance and investing, highlighting
the balance between the desire for the lowest possible risk and the highest possible returns.
Investors must decide how much risk they are willing to tolerate for a given level of return. Low
risk often equates to low returns, while high-risk investments offer the potential for higher
returns.

Returns cannot be separated from risk. Investors first decide about the level of risk, then the
objective should be maximization of return for that level of risk. To calculate an appropriate risk
return tradeoff, investors must consider many factors, including overall risk tolerance, the
potential to replace lost funds, and more.

RISK:
Risk in finance refers to the uncertainty or variability of returns from an investment or decision.
Itrepresents the possibility that the actual returns or outcomes will deviate from the expected
ones, potentially leading to financial loss. Understanding and managing risk is critical to making
informed financial decisions. The level of risk differs from security to security, thus it is
advisable to research before investing in any securities. While risk can lead to gains, it often
emphasizes the potential for losses. Risk arises due to unknown factors that can impact the outcome
both externalor internal to the company which issues the securities.
Types of risk:
1. Systematic Risk
It is the type of risk that affects the entire market or a broad range of assets. It is inherent
tothe overalleconomy and cannot be eliminated through diversification. Systematic risk
is also known as non-diversifiable risk as the risk cannot be diversified by holding a
large number of securities. It is inherent tothe overall economic, political, or social
system and cannot be mitigated through diversification; it is driven by external,
uncontrollable factors.
Sources of Systematic risk includes
a) Market Risk- It refers to the potential for losses or fluctuations in the value of an
investment due to changes in the overall market conditions.
 b) Interest Rate Risk- The risk of losses due to changes in interest rates, primarily
affecting fixed-income investments like bonds.
c) Inflation risk- The risk that rising inflation willerode the purchasing power of money
and reduce real returns. It is common in fixed-income securities.
d) Exchange Rate Risk-The risk of losses due to fluctuations in exchange rates,
particularly in international investments. Companies with global operations face risks
from currency volatility.

2. Unsystematic Risk
Unsystematic risk, also known as diversifiable risk, refers to the risk that is specific toa
particular company, industry, or sector. Unlike systematic risk, it does not affect the
entire market and can be mitigated through diversification by holding an efficient
portfolio of securities which are least correlated. It arises from factors unique to a
company or industry, such as operational issues or regulatory changes. Unsystematic risk
is not linked to broad market movements and arises from micro-level factors.
Sources of Unsystematic risk includes
a) Business Risk-It is associated with the investment decision of a company. The risk
which arises due to the presence of fixed operating costs in a company's cost structure.
b) Financial Risk- It is associated with financing decisions or capital structure of a
company. It arises due to the presence of fixed financial cost or debt capital in a
company.

Types ofrisk

Systenmatic Unsystematic
Risk Rislk
Market Risk +Business Risk
Interest Risk Pinancial Risk
Inflation Risk
Exchange Rate
Risk

Types of investors
1. Risk Averse Investors: Risk-averse investors prioritize the safety of their capital over
the potential for high returns. They are willing to accept lower returns to avoid risk and
uncertainty.
 2. Risk Neutral Investors: Risk-neutral investors evaluate investments purely based on
potential returns, without considering the risk involved, They focus on maximizing
expected returns regardless of the levelof risk.
3. Risk lover Investors: Risk-loving investors are willing to take on higher risks for the
possibility of higher returns. They focus on growth and are comfortable with volatility
and uncertainty.

Types oflnvestors

RiskAvcrse
Investor
Risk Seutral
Investo
Risk lover
nvestor

Calculation of Total Risk

Total Risk is the measure of the variability or uncertainty of returns on an investment. It is
typically expressed as the standard deviation of the investment's returns.
Therefore total risk on a security can be measured by using statistical methods of measuring
variability or such as Range, Standard Deviation (SD) or variance.
Mean Return ():
Ri/n
where, Ri=the return in period
n= the total number of periods.
Variance-X(Ri-u'/n
Where, Ri= i-th return
= Mean Return
Standard Deviation
6-VVariance
Here, o represents the total risk.

EXAMPLE

Suppose an investment has the following annual returns over the last 5 years:
 Year Return (%)
8

2 12

3 10

4 15

5 5

Mean Return
-Ri/n
- (8+12+10+15+5)/5
=50/5=10%

Year Return (%) (Ri-uy)?

(8-10)?=(-2)'=4
2 12 (12-10)-(2)'=4
3 10 (10-10=(0=0
4 15 (15-10=(5)'=25
5 (5-10)-(-5)?=25
Total =50 XRi-u'-58

Variance=2(Ri-u'/n
= 58/5
= 14.5
g=Wariance =V14.5=3.81

approximately 3.81%.
The total risk (standard deviation of returns) is
Risk
Coefficient of Variation: A relative measure of
(volatility) relative to the expected return
It is a statistical measure used to assess the level of risk
risk-return trade-off across different
of an investment. It helps investors compare the
investments.
 CV =
Standard Deviation of Returns(o )
Mean Return(4)

Where:

o: Standard deviation of the returns (a measure of risk).

: Mean (average) return of the investment.
A lower CV indicates a better risk-return trade-off (less risk per unit of return).

EXAMPLE:

Comparing two investments with the following statistics:

Investment Mean Return(u) Standard Deviation (o)

A 10% 5%

B 12% 8%

Investment A:
CVA=o/H
=5%/10%
=0.5
Investment B:
CVB-o/!
=8%/12%
0.67

Investment A has a lower CV (0.5), meaning it has less risk per unit of return compared to
Investment B (0.67).
RETURN:
Return refers to the gain or loss generated on an investment over a specific period, expressed
either as a percentage of the investment's initial value or as an absolute amount. lt measures the
profitability or performance of an investment and is a key indicator used by investors to evaluate
and compare different investment opportunities, Like earnings from the asset, such as dividends
from stocks,interest from bonds,or rental income from realestate are part of the retum.
Components of Return are - Capital Gains: The profit or loss from changes in the asset's price.
Income: Earnings from the asset, such as dividends from stocks, interest from bonds, or rental
income from real estate.

Return= | Income from asset + (Selling price - Purchase price)/ Purchase Price ] x 100

Return on equity share- D1+ (Pi-Po)/ Po

Where, D, =Dividend Received at the end of the year
Po = Cost of Investment or Share Price in the beginning of the year
P,= Share Price at the end of the year

Expected Return (based on probability distribution)

Expected Return is the weighted average of all possible returns of an investment, where the
weights are the probabilities of each outcome occurring. It helps investors anticipate the potential
return from an investment, factoring in the likelihood of different scenarios. Security analysts
can actually construct a probability distribution of returns by assigning probabilities to the
expected return outcomes.
Expected Return= E(R)-X(PixRi)
Where,
Pi= Probability of the i-th outcome.
Ri = Return to the i-th outcome.
EXAMPLE:
Suppose an investor is considering an asset with the following potential returns and their
associated probabilities:
Return (Ri) Probability (Pi)
10% 0.30

15% 0.40

20% 0.30

The expected return can be calculated as:

E(R}F(0.30x10%+(0.40x15%)+(0.30×20%)
 E(R) =0.03 +0.06+0.06 = 0.15
Thus, the expected return is 15%.

Expected Return (based on Capital Asset Pricing Model (CAPM))

The Capital Asset Pricing Model (CAPM) provides away to calculate the expected return on an
asset, considering the asset's risk relative to the market. It is based on the asset's sensitivity to
market movements (measured by beta) and the risk-free rate, along with the expected market
return. As per CAPM there isa positive and linear relationship between expected return and
systematic risk as measured by beta.
Beta measures the volatility or risk of the asset in relation to the overall market.
If B=1, the asset moves in line with the market.
If>1,the asset is more volatile than the market (higher risk, higher return potential),.
If B<1, the asset is less volatile than the market (lower risk, lower return potential).
E(Ri-Rf+Bix(E(Rm)-Rf)

Where, E(Ri) = Expected return of the asset.

Rf= Risk-free rate (typically the return on government bonds).

B=Beta of the asset (measures its sensitivity to market movements).
E(Rm) = Expected return of the market.

E(Rm)-Rf= Market risk premium (additional return expected from investing in the
market rather than the risk-free asset).

EXAMPLE:

Calculate the expected return for a stock with the following values:

Risk-free rate (Rf) =4%

Beta of the stock (Bi) = 1.2

Expected market return E(Rm)- 10%

Using the CAPM formula:

E(Ri)=Rf+Bix(E(Rm)-RA)
E(Ri)-4%+1.2x(10%-4%)
E(Ri)=4%+1.2x6%
E(Ri)=4%o+7.2%=11.2%
 Thus, the expected return on this stock, according to CAPM, is 11.2%.
Return of a Portfolio
Return on a portfoliois the overallgain or loss generated by all the assets within a porttolioover
aspecific period. It reflects the combined performance of the individual investments, weighted
by their proportionate value in the portfolio.
Portfolio Returns is the weighted average of the returns on individual securities, weights being
the proportion of funds invested in each security.

The return on a portfolio (Rp) is calculated as the weighted average return of all the assets in the
portfolio:
Rp-2(WixRi)
Where:

Rp = Portfolio return.
Wi= Weight of the i-th asset in the portfolio
Ri= Return of the i-th asset.
The summation is across all assets in the portfolio.
EXAMPLE:

Suppose an investor holds the following portfolio:

Asset Investment Value () Return (Ri)

Stock A 50000 10%

Stock B 30000 8%

Stock C 20000 12%

Asset Investment Value () Return (Ri) Weights (Wi) Weighted Return (Wi Ri)
Stock A 50000 10% 50000/100000=0.50 0.50×10%=5%
Stock B 30000 8% 30000/100000=0.30 0.30×8%-2.4%
Stock C 20000 12% 20000/100000=0.20 0.20x12%-2.4%
Total =100000 XWi Ri=9.8%

Final Portfolio Return: The return on the portfoliois 9.8%.