by- g 6 envensebles
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Dip Murmu & Md. Abadullah Miah
Neamur Rabbi & Md. Azad Khan
Anik Costa & Tanvir Hasan Plabon
Tarikul Islam Tarif
Md. Jakir Hossain Khan & Dilruba Jahan
Shanjida Afrin & Md. Rajib
by- g 6 envensebles
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Dip Murmu & Md. Abadullah Miah
Neamur Rabbi & Md. Azad Khan
Anik Costa & Tanvir Hasan Plabon
Tarikul Islam Tarif
Md. Jakir Hossain Khan & Dilruba Jahan
Shanjida Afrin & Md. Rajib
Risk and Return: Portfolio Theory and Assets Pricing ModelsPANKAJ PANDEY
Discuss the concepts of portfolio risk and return.
Determine the relationship between risk and return of portfolios.
Highlight the difference between systematic and unsystematic risks.
Examine the logic of portfolio theory .
Show the use of capital asset pricing model (CAPM) in the valuation of securities.
Explain the features and modus operandi of the arbitrage pricing theory (APT).
In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.
All related information about Cost of capital and investment theory for instance, weighted average cost of capital (WACC), cost of debt, cost of equity, investment theories and so on.
This is the fifth presentation for the University of New England Graduate School of Business course GSB711 Managerial Finance, offered by Dr Subba Reddy Yarram. This presentation examines risk, return and the Capital Asset Pricing Model (CAPM).
Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night.
Importance of wacc and npv on investment decisionsCharm Rammandala
The purpose of this article is to understand the importance of Weighted Average Cost of Capital and Net Present Value have on the investment decisions. It is vital to ensure all the investment decisions are done after looking at the viability of the investment opportunity and whether it is increasing the shareholder value by exceeding the opportunity cost. This study will primarily look in to the role played by WACC and NPV on the investment decisions.
Risk and Return: Portfolio Theory and Assets Pricing ModelsPANKAJ PANDEY
Discuss the concepts of portfolio risk and return.
Determine the relationship between risk and return of portfolios.
Highlight the difference between systematic and unsystematic risks.
Examine the logic of portfolio theory .
Show the use of capital asset pricing model (CAPM) in the valuation of securities.
Explain the features and modus operandi of the arbitrage pricing theory (APT).
In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.
All related information about Cost of capital and investment theory for instance, weighted average cost of capital (WACC), cost of debt, cost of equity, investment theories and so on.
This is the fifth presentation for the University of New England Graduate School of Business course GSB711 Managerial Finance, offered by Dr Subba Reddy Yarram. This presentation examines risk, return and the Capital Asset Pricing Model (CAPM).
Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night.
Importance of wacc and npv on investment decisionsCharm Rammandala
The purpose of this article is to understand the importance of Weighted Average Cost of Capital and Net Present Value have on the investment decisions. It is vital to ensure all the investment decisions are done after looking at the viability of the investment opportunity and whether it is increasing the shareholder value by exceeding the opportunity cost. This study will primarily look in to the role played by WACC and NPV on the investment decisions.
What Is a Business Plan? What's right time to develop the Business Plan?. Reasons of Developing a Business Plan. Guidelines for Writing a Business Plan. How long and detailed should it be?. Types of Business Plans. Guidelines for Writing a Business Plan. Outline of Business Plan
Basic terms review
Capital budgeting introduction
Capital budgeting technique
Sensitivity analysis
Scenario analysis
present value
potential difficulties and strength of capital budgeting
basic financial analysis, framework for ratio analysis, types of ratio analysis, liquidity ratios, debt ratios, equity ratios, activity ratios, profit ratio, index analysis, common size financial statements
Feasibility Analysis
Feasibility analysis is the process of determining whether a business idea is viable.
It is the preliminary evaluation of a business idea, conducted for the purpose of determining whether the idea is worth pursuing.
Feasibility analysis takes the guesswork (to a certain degree) out of a business launch, and provides an entrepreneur with a more secure notion that a business idea is feasible or viable.
Comprehensive Feasibility Analysis, Product/Service Desirability
The Importance of Getting Financing or Funding, Sources of Personal Financing, Examples of Bootstrapping Methods, Alternatives for Raising Money for a New Venture, Preparing to Raise Debt or Equity Financing, Sources of Equity Funding
industry, Industry Analysis, Why is Industry Analysis Important? How Industry and Firm-Level Factors Affect Performance, Techniques Available to Assess Industry Attractiveness, Studying Industry Trends
Marketing plan and its steps. Selecting a Market and Establishing a Position in the Market. The Process of Selecting a Target Market and Positioning Strategy. branding. marketing mix. launch of product
developing a business model. business model innovation. types of business model. How Business Models Emerge. Components of a Business Model. core strategy, strategic resources
Ch5 Portfolio Theory -Risk and ReturnLiang (Kevin) Guo.docxketurahhazelhurst
Ch5 Portfolio Theory -Risk and Return
Liang (Kevin) Guo
Learning Objectives
Be able to calculate ex post and ex ante risk and return statistical measures, such as holding period return, average returns, expected returns, and standard deviation.
Understand the difference between time-weighted and dollar-weighted returns, geometric and arithmetic averages.
Be able to construct portfolios of different risk levels, given information about risk free rates and returns on risky assets.
Be able to explain the CML theory.
Table of Contents
5.1 Rates of Return
5.2 Risk and Risk Premiums
5.3 Inflation and Real Rates of Return
5.4 Asset Allocation Across Risky and Risk Free Portfolios
5.5 Passive Strategies and The Capital Market Line (CML)
5.1 Rates of Return
Considering one-single period investment: regardless of the length of the period.
Holding period return (HPR): measuring Ex-Post (Past) Returns over one-single period.
HPR = [PS - PB + CF] / PB
where
PS = Sale price (or P1)
PB = Buy price ($ you put up) (or P0)
CF = Cash flow during holding period ( Such as dividend, interest)
Example: You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. What is your HPR?
Annualizing HPRs
Annualize a holding period return: translate it into percentage per year.
(1) Without compounding (Simple or APR):
HPRann = HPR/n
(2) With compounding: EAR
HPRann = [(1+HPR)1/n ]-1
where n = number of years held
Annualizing HPRs for holding periods of greater than one year
Example: Suppose you buy one share of a stock today for $45 and you hold it for two years and sell it for $52. You also received $8 in dividends at the end of the two years. What is the annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n =2 ):
(
Annualizing HPRs for holding periods of less than one year
Example: Suppose you buy one share of a stock today for $45 and you hold it for 3 months and sell it for $52. You also received $8 in dividends at the end of the two years. What is the annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n =0.25 ):
Investment Returns over multiple periods
The holding period return (HPR) is a simple measure of investment return over a single period.
But how to measure the performance of a mutual fund over the last ten-year period?
Several measures to find the average investment return for a time series of returns .
(a) Arithmetic average return (simple Time-weighted average)
(b) Geometric average return (Geometric time-weighted average)
(c) Dollar-weighted return
(a) Arithmetic Average Return (AAR)
(a) Arithmetic average (simple Time-weighted average)
Arithmetic means are the sum of ...
time value of money, future value with exercises, present value exercises. annuity, annuity due exercises, mixed flows, rule of 72 with exercise, unknown interest rate and time period with exercises. present value and future value with discounting monthly, quarterly, semi-annually, annually etc
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measurement and scaling is an important tool of research. by following the right and suitable scale will provide an appropriate result of research.this slide show will additionally provide the statistical testing for research measurement and scale.
measurement and scaling are very important components for data collection. using the right and appropriate sale is an important aspect of right directed research. additionally, this slide show helps the research to select the suitable statistical test in the reseach
problem definition in research has the basic role in research, hence, this presentation pertaining to identification of problem by the use of different method
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
1. Risk Return: lecture 5
Capital Asset Pricing model
By Muhammad Shafiq
forshaf@gmail.com
http://www.slideshare.net/forshaf
2. Variability and business risk
• a situation involving exposure to danger.
• It is the variability that a business firm experiences over time in its
income. Some firms, like utility companies, have relatively stable
income patterns over time.
• The variability of returns from those that are expected.
• Business risks implies uncertainty in profits or danger of loss and the
events that could pose a risk due to some unforeseen events in
future, which causes business to fail.
3. Averse of business risk
• A risk averse investor is an investor who prefers lower returns with
known risks rather than higher returns with unknown risks.
• A risk averse investor is an investor who prefers lower returns with
known risks rather than higher returns with unknown risks.
4. Risk management
is the identification, assessment, and prioritization of risks followed by
coordinated and economical application of resources to minimize,
monitor, and control the probability and/or impact of unfortunate
events or to maximize the returns
5. Risk premium and risk free interest rate
For an individual, a risk premium is the minimum amount of money by
which the expected return on a risky asset must exceed the known
return on a risk-free asset in order to induce an individual to hold the
risky asset rather than the risk-free asset.
• Risk-free interest rate is the theoretical rate of return of an
investment with no risk of financial loss.
• the risk-free rate represents the interest that an investor would
expect from an absolutely risk-free investment over a given period of
time.
•
6. Risk-free interest rate
• Risk-free interest rate is the theoretical rate of return of an
investment with no risk of financial loss. One interpretation is that
the risk-free rate represents the interest that an investor would
expect from an absolutely risk-free investment over a given period of
time.
•
7. covariance
• In probability theory and statistics, covariance is a measure of how
much two random variables change together.
• Covariance indicates how two variables are related. A positive
covariance means the variables are positively related, while a negative
covariance means the variables are inversely related. The formula for
calculating covariance of sample data is shown below.
8. Day ABC Returns (%) XYZ Returns (%)
1 1.1 3
2 1.7 4.2
3 2.1 4.9
4 1.4 4.1
5 0.2 2.5
Table: Daily returns for two stocks using the closing prices
Calculating Covariance
Calculating a stock's covariance starts with finding a list of previous prices. This is labeled as
"historical prices" on most quote pages. Typically, the closing price for each day is used to find the
return from one day to the next. Do this for both stocks, and build a list to begin the calculations.
For example:
From here, we need to calculate the average return for each stock:
For ABC it would be ( 1.1+1.7+2.1+1.4+0.2/ )5=1.30
For XYZ it would be ( 3+4.2+4.9+4.1+2.5/ )5=3.74
Now, it is a matter of taking the differences between ABC's return and ABC's average return, and
multiplying it by the difference between XYZ's return and XYZ's average return. The last step is to
divide the result by the sample size and subtract one. If it was the entire population, you could just
divide by the population size.
This can be represented by the following equation :
Using our example on ABC and XYZ above, the covariance is calculated as:
=[(1.1-1.30( x )3-3.74([ + ])1.7-1.30( x )4.2-3.74([ + ])2.1-1.30( x )4.9-3.74])+…
[ =0.148[ + ]0.184[ + ]0.928[ + ]0.036[ + ]1.364]
=2.66( /5-1)
=0.665
9. Returns
A return is the gain or loss of a security in a particular period.
The return consists of the income and the capital gains relative on an
investment. It is usually quoted as a percentage
The amount one would anticipate receiving on an investment that has
various known or expected rate of return
10. Portfolio
• a range of investments held by a person or organization
• A portfolio is a grouping of financial assets such as stocks, bonds and
cash equivalents, as well as their mutual, exchange-traded and
closed-fund counterparts.
• Portfolios are held directly by investors and/or managed
by financial professionals.
• Portfolio management is the art and science of making decisions
about investment mix and policy, matching investments to objectives,
asset allocation for individuals and institutions, and balancing risk
against performance
11. In finance and economics, nominal rate refers to
the rate before adjustment for inflation (in contrast
with the real rate). The real rate is the nominal
rate minus inflation. In the case of a loan, it is
this real interest that the lender receives as
income.
12. Century performance of Capital Market in US
• Plenty of data for financial analysts
• Focusing on the prices of stock, bonds, options and commodities:
• Portfolio of treasury bills (safe investment, no risk of default)
• Portfolio of US government bonds(ups and down due to interest rate
fluctuation)
• Portfolio of US common stock (more risk and more yield)
• Reasons are fluctuations in common stock growth
Average annual rate of return since 1900 to 2011
Average risk premium (extra return v/s treasury billsRealNominal
01.03.9Treasury bills
1.42.55.4Government bonds
7.38.211.3Common stocks
13. Arithmetic Average and compound annual returns
• An arithmetic average is the sum of a series of numbers divided by
the count of that series of numbers. If you were asked to find the
class (arithmetic) average of test scores, you would simply add up all
the test scores of the students, and then divide that sum by the
number of students
• This is the rate of return which, if compounded over the years
covered by the performance history, would yield the cumulative gain
or loss actually achieved by the trading program during that period.
• Arithmetic averages are higher than the compound annual return
• e-g 112 years annual compound returns for S&P Index9.3% while Kse 35-years
index on arithmetic basis was 17.55%
14. Arithmetic Average and compound annual returns
• Suppose oil company Common Stock Price Rs.100. chances are that
the end of the year it might be Rs. 90, Rs. 110 or Rs. 130.
The expected return could be [1/3(-10+10+30)]= + 10
Or -10+10+30/3 =10%
• On discount or compound cash flow it will be as:
PV= 110/1.10= Rs. 100 (expected rate of return 10%)
• Average compound returns of oil company as:
(.9*1.1*1.3)1/3 =.088 or 8.8%
NPV at 10% = -100+108.8/1.1 = -1.1
15. Using historical evidence to evaluate today’s cost of capital
• Suppose you have a project having the same risk as in the market portfolio,
what rate to discount the project would have.
How would you calculate?
• Use currently expected rate of return on the market portfolio
• If market return is rm, we assume that present is like past.
• To know exactly the rm , remember sum of the risk free interest rate rf
(7.3%)and a premium for risk (11.92%)
Solution rm (2016)= rf (2016)+normal risk premium
=.0731+0.1192
=19.23%
• Normal and stable risk premium on market portfolio to measure the
expected future risk premium(example of US investors)
16. Using historical evidence to evaluate today’s cost
of capital
Suppose that stock is expected to pay a dividend next year of Rs 12
(DIV=12). The stock yields 3% and the dividend is expected to grow
indefinitely by 7% a year (g=.07). Therefore, the total return that investors
expect is r=3+7=10%. We can find the stock’s value by plugging these
numbers into constant growth formula as
PV=DIV1/(r-g)
=12/(.10-.07)
=Rs. 400
Imagine that investors now revised downward their required return r=9%.
The dividend yield falls to 2% and the value of stock rises to
PV=DIV1/(r-g) = =12/(.09 - .07) =Rs. 600
17. MEASURING PORTFOLIO RISK
• Two point important:
How to measure risk
• The relationship between risk borne and risk premiums demanded
• Important tools can be
• Variance
• Standard deviation
• Variability
• etc
18. Variance and standard deviation
• Measure of spread are variance and standard deviation.
• Variance of the market return is the expected squared deviation from
the expected return
• Variance (r-
m)= expected value of (r-
m - rm)2
Where r-
m is the actual return and rm is the expected return
• Standard deviation is the simple squared root of variance
Standard Deviation of r-
m = variance (r-
m)squared root
19. Variance and standard deviation
• Example:
You start by investing Rs. 100. then two coins are flipped. For each head that
comes up you get back your starting balance plus 30% and for each tail that
comes up you get back your starting balance less 10%. Clearly there are four
possible outcomes.
Head+ head you gain 60%
Head+ tail: you gain 20%
Tail + head: you gain 20%
Tail + tail: you lose 20%
There is a chance of 1 in 4 or .25 that you will make 60%; a chance of 2 in 4
or .5 that you will make 20% and chance if 1 in 4 or 0.25, that you lose 20%.
The game’s expected return is, therefore, a weighted average of the possible
outcomes:
Expected return= (.25*60)+(.5*20)+ (.25*-20) =+20%
20. The coin tossing game: calculating variance and standard deviation
(5) Probability
squared deviation
(4) probability(3) Squared dev
(r- - r)2
(2) Dev from exp ret
(r- -r)
(1) 1 % RoR ( r-)
4000.251600+40+60
00.500+20
4000.251600-40-20
Variance = expected value ((r- - r)2 =800
Standard deviation = variance squared = 800 squared = 28.28
21. Measuring the variability
• Variability can simply be measured by variance or deviations.
• Newspapers and stock brokers are the source
• Past market movement
22. How diversification reduces risk
• Market portfolio is made up of individual stocks
• Diversification reduces variability
• Little diversification provides substantial reduction in variability
• Diversification works because prices of different stocks do not move
exactly
23. Risk
• Risk that potentially can be eliminated by diversification is called
specific risk
• Market risk stems from the fact that there are other economy wide
perils that threaten all business, hence, a firm can not reduce it
Specific risk
Market risk
24. Calculating portfolio risk
• Suppose 58% of your portfolios invested in PTCL and remainder is
invested in PSO . You expect over the year PTCL will give a return of
13% and PSO 19%. The expected returns on your portfolio is simply a
weighted average of the expected returns on the individual stocks:
expected portfolio returns= (0.58*.13)+ (.42*19) = 15.52%
Assume that the SD of portfolio is weighted average of the SD of two
stocks:
that is = (0.58*33.5) + (0.42*46.5)= 38.96%z
25. Calculating the risk of two stock portfolio from the figure as
you weight the variance of the returns on stock1 (sig sq) by the square of the proportion
invested in it (x21).
Similarly to complete the bottom right box, you might the variance of the returns on stock 2
(sig) by the square of the proportion invested in stock 2(x2
2)
In case the correlation coefficient p12 is positive and therefore the covariance σ12 is also
positive
X1X2 σ2
12
= X1X2 P12 σ1 σ2
X2
1 σ2
1
X2
2 σ2
2X1X2 σ12
= X1X2 P12 σ1 σ2
Stock 1
Stock 1 Stock 2
Stock 2
26. Calculating portfolio risk
If the prospects of the stocks tended to move in opposite directions,
the correlation coefficient and the covariance would be negative
Just as you weighted the variances by the square of the proportion
invested so you must weight the covariance by the product of the two
proportionate holdings x1 and x2
Portfolio variance= = X2
1 σ2
1 + X2
2 σ2
2 + 2( X1X2 P12 σ1 σ2)
Portfolio SD is square root of the variance
27. Calculating portfolio risk
• We can the same in example of PTCL and PSO. We said earlier the two
stock were perfectly correlated, the SD of the portfolio would lie 58%
of the way between the SD of the two stocks
• The variance of your portfolio is the sum of these entries:
Portfolio variance = [(0.58)2 *(33.5)2]+ [(0.42)2* (46.5)2+2(0.58*42*1*33.5*46.5)=
1516.99
• SD= 38.95
PSOPTCL
= X1X2 P12 σ1 σ2
=(0.58)*0.42*1*(33.5)*(46.5)
X2
1 σ2
1 =(0.58)2 *(33.5)2PTCL
X2
2 σ2
2
=(0.4)2 * (46.5)2
= X1X2 P12 σ1 σ2
=(0.58)*(0.42)*1*(33.5)*(46.5)
PSO
28. How individual securities affect portfolio risk
• The risk of well diversified portfolio depends on the market risk of the
securities included in the portfolio
• Market risk measured by beta
• Beta is sensitivity (B)
• Beta remains between 0 and 1.0
• Individual securities reacts to overall change in the market
• Higher the beta more the riskier the securities
29. Why security betas determine portfolio risk
Two crucial points about security risk and portfolio risk
• Market risk accounts for most of the risk of a well-diversified portfolio
• The beta of an individual security measures it sensitivity to market
movement
calculating beta Bi = σim / σ2
m
σim = covariance between the stock returns and the market returns and
σ2
m is the variance of the return on the market