FIN 301 SEU Risk Management Worksheet


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College of Administrative and Financial Sciences
Assignment 3
Risk Management (FIN301)
Deadline for students: (22/04/2022@ 23:59)
Course Name: Risk Management
Student’s Name:
Course Code: FIN301
Student’s ID Number:
Semester: 2nd
Academic Year: 1443/1444 H, Second Semester
For Instructor’s Use only
Instructor’s Name:
Students’ Grade: /5
Level of Marks: High/Middle/Low
❖ This assignment is an individual assignment.
❖ The Assignment must be submitted only in WORD format via the allocated
❖ Assignments submitted through email will not be accepted.
❖ Students are advised to make their work clear and well presented. This also
includes filling in your information on the cover page.
❖ Students must mention question numbers clearly in their answers.
❖ Late submitted assignments will NOT be entertained.
❖ Avoid plagiarism; the work should be in your own words; copying from
students or other resources without proper referencing will result in ZERO
marks. No exceptions.
❖ All answered must be typed using Times New Roman (size 12, doublespaced) font. No pictures containing text will be accepted and will be
considered plagiarism).
Submissions without this cover page will NOT be accepted.
Assignment Questions:
(Marks: 05)
Q1: Briefly explain three key goals of Asset/Liability Management (ALM)? (1.5 Marks)
Q2: Discuss four Purposes of the Internal Risk Rating System (IIRS)? (2 Marks)
Q3) What is the difference between default and bankruptcy? (1.5 Marks)
Chapter 1
Introduction to Risk Management
What is Risk?
ƒ The future cannot be predictable. It is uncertain, and no one
has ever been successful in forecasting the stock market,
interest rate or exchange rate consistently.
ƒ Yet, the financial risk that arises from uncertainty can be
ƒ Understanding risk on the basis of expected loss and
unexpected loss.
ƒ Expected loss: As it is predictable, generally viewed as one of
the costs of doing business and ideally it is priced into the
products and services offered to the customers.
What is Risk?
ƒ Unexpected loss: Risk is primarily associated with
unexpected loss. The risk that are lumpy (in large
block, such as very large loan) and that are driven by
risk factors that under certain circumstances can
become linked together, we can predict that at certain
times high unexpected losses will be realized.
Types of Risks
Market risk
Credit Risk
Liquidity Risk
Operational Risk
Legal and regulatory Risk
Business Risk
Strategic Risk
Reputation Risk
Market Risk
ƒ Market Risk: Risk that changes in financial market prices and
ƒ Market risk includes:
portfolio value due to interest rate fluctuations.
ƒ Equity Price risk: It refers to the sensitivity of an instrument
or portfolio value associated with volatility in stock market.
ƒ Foreign exchange Risk: Risk arises due to fluctuations in
foreign exchange rates.
Credit risk
ƒ Credit risk: Risk that a change in the credit quality of a
ƒ Liquidity Risk: Includes both funding liquidity risk and asset
liquidity risk.
ƒ Funding liquidity risk relates to a firm’s ability to raise the
necessary cash to roll over its debt, to meet the cash, margin
and collateral requirements of counter parties.
ƒ Asset liquidity risk: it is risk when institution is not in a
position to execute a transaction at prevailing rate.
Operational risk:
ƒ Operational risk: Refers to potential losses resulting
from inadequate systems, management failure, faulty
controls, fraud, and human errors.
ƒ Legal and regulatory risks: Usually become
apparent when an counterparty or investor loses
money on a transaction and decides to sue the bank to
avoid meeting obligations.
ƒ Human risk factor: Relates to the losses that may
result from human errors.
Business risk
ƒ It refers to the classic risk of the world of business,
such as uncertainty about the demand for products,
the price that can be charged for those products or the
cost of producing and delivering products.
ƒ Strategic risk: Strategic risk refers to the risk of
significant investments for which there is a high
uncertainty about success and profitability. If the
venture is not successful, then the firm will usually
suffer a major write-off, and its reputation among
investors will be damaged.
ƒ Reputational risks: It refers to the potential adverse
deviating negatively from its expected level.
ƒ Systemic risks: Risk of the collapse of the banking
industry at the regional, national, or international
ƒ Residual risks: The residual risk is the amount of
risk associated with an action or event remaining after
natural or inherent risks have been reduced by risk
ƒ Settlement risks: Settlement risk is the possibility
that one or more parties will fail to deliver on the
terms of a contract at the agreed-upon time.
Settlement risk is a type of counterparty risk
associated with default risk.
ƒ Country risks: Country risk refers to the uncertainty
associated with investing in a particular country, and
more specifically the degree to which that uncertainty
could lead to losses for investors
The Need for Risk Management Systems
‡ Two problems with risk
¾ Quantifying
¾ Pricing
‡ Banking industry
¾ Biggest risk is credit risk: Credit risk is most simply defined
as the probability that a bank borrower or counterparty will fail to
meet its obligations in accordance with agreed terms.
The Need for Risk Management Systems
‡ Reasons for risk
¾ Banks trade all types of cash instruments and
¾ These derivatives include:
¾ Swaps
¾ Forward contracts
¾ Options for their own account or to facilitate
customer transactions.
The Need for Risk Management Systems
‡ Regulation affects the attitude of financial institutions
toward risk taking.
‡ Regulation often affects how financial institutions
accommodate risk.
‡ Two observations on risk can be stated:
¾ World-wide recognition of the need to measure and
control risk in global and local banking activities.
¾ Regulation is becoming more consistent across
The Need for Risk Management Systems
‡ Domino effect
¾ Chance that a failure by one bank will lead to
failure at another bank and another and so on.
¾ To avoid this situation, the government tried to
increase the stability of the banking system.
¾ 1933, the establishment of the Federal Deposit
Insurance Corporation (FDIC) to protect deposits.
The Risk Management Process
The Risk Management Required following Steps:
Identify risk exposures
Measure and estimate risk exposure
Find instruments and facilities to shift or trade risksAssess costs and benefits of instruments
ƒ Assess effects of exposures
ƒ Form a risk mitigation strategy: Avoid, Transfer,
Mitigate, Keep
ƒ Evaluate performance
Corporate Risk Management
‡ Nonfinancial companies are exposed to many traditional business
risks like, earning fluctuations, new competitors, new production
technologies and weakness in supply chains.
‡ Firms use to manage these risk in many ways, for example: by holding
inventories of raw materials, by storing finished products, signing
long-term supply contracts at fixed price, or even by conducting
mergers with competitors, distributors and suppliers.
In this chapter, we will focus on:
More specific and relatively novel, aspect of enterprise risk management.
Why and how should a firm choose to hedge the financial risks.
The practical decisions a firm must make if it decides to engage in active
risk management.
‡ The problem of how the board sets the risk appetite of a firm?
and the selection of risk management tactics.
‡ How exposures can be tackled using a variety of risk management
Why Not to Manage Risk in Theory..
‡ We will start the discussion by going through the famous analysis laid
out by two professors, Franco Modigliani and Merton Miller(M&M) in
‡ It shows that in a perfect capital market, with no corporate or income
taxes, the capital structure of a firm has no effect on the value of the
‡ M&M reasoned that whatever the firm can accomplish in the
financial markets, the individual investor in the firm can also
accomplish on the same terms and conditions.
‡ This line of reasoning has also been reflected in the work of William Sharpe, in his
capital asset pricing model(CAPM), William Sharpe established that in a world of
perfect markets, firms should not worry about the risks that are specific to them,
and should base their investment decisions only on the risks they hold common
with other companies( known as systematic or beta risks).
‡ Those opposed to active corporate risk management often argue:
‡ That hedging is a zero-sum game and cannot increase earnings or cash flows.
‡ That reducing volatility through hedging simply moves earnings and cash flows
from one year to another.
‡ That the prices of derivatives fully reflect their risk characteristics, therefore using
such instruments cannot increase the value of the firm in any lasting way.
‡ Besides the theoretical arguments there are also some practical objections,
against the use of derivatives for risk management.
‡ Active hedging may distract management from its core business.
‡ Risk management requires specialized skills, knowledge and infrastructure.
‡ A risk management strategy that is not carefully structured and monitored
can drag a firm down even more quickly then the underlying risk.
‡ A well developed risk management strategy has compliance costs,
including disclosure, accounting and management requirements.
‡ Firms may avoid trading in derivatives in order to reduce such costs or to
protect confidential information.
Some reasons for Managing risk in practice
‡ The assumption that capital markets operate with perfect efficiency
does not reflect market realities.
‡ Manager have an interest in reducing risks, whether or not they have
a large personal stake in the firm, because the results of a firm
provide a signals to boards and investors concerning the skills of its
‡ In case of progressive tax rate, volatile earnings induce higher
taxation than stable earnings.
‡ Hedging increases the debt capacity of companies, which in turn
increases tax deductions.
‡ By employing risk management tools, management can better achieve the
boards objective.
‡ Hedging reduces the cost of capital and enhance the ability to finance
costs of its activities.
‡ Conclusion: There are arguments both in favour and against the risk
management practice by corporate sector. From the discussion we can
conclude that, we should not take granted that risk management strategies
are good thing, but instead should examine the logic of the argument in
relation to the specific circumstances and aims of the firm and its
Putting Risk Management into Practice
‡ Determining objective: A corporation should not engage in risk
management before deciding clearly on its objectives in terms of risk
and return.
‡ The first step in this process is to determine the risk appetite of the
firm as the board defines it. The risk appetite can be expressed in
quantitative( Financial targets, like capital adequacy, target debt
rating, earning volatility etc.) or qualitative statement( reputational
impact, management effort and regulatory compliance).
should be hedged and which risks the company should assume as
part of its business strategy.
‡ The next step for the board is to decide time horizon for any of the
risk management objectives for management.
‡ Another important objective for the board is to decide, risk limit ,
that is to allow management to operate within a range of risk.
‡ Mapping the risk: After the objectives have been set, the next step is
to map the relevant risks and to estimate their current and future
‡ When mapping the risk, it is important to differentiate between the
risk which can be insured, risks that can be hedged and risk that are
non insurable and non hedgable.
‡ Instruments for Risk Management: After mapping the risks, the next
step is to identify instruments that can be used risk-manage the
‡ Next, the company should compare competing ways to manage the
risks that have been identified as transferable or insurable in the riskmaping process, and evaluate likely costs and be befits.
‡ Some of the instruments can be devised internally and some can be
picked up from the plenty financial instruments for hedging risks that
have been developed over the last few decades.
Constructing and implementing a strategy
‡ The office of CFO must have access to all the relevant corporate
information, market data, and statistical tools and models before
attempting to devise a hedging strategy.
‡ In a static strategy, a hedging instrument is purchased to match the
risky position as exactly as possible and is maintained for as long as
the risky position exists.
‡ Dynamic strategy is involve an ongoing series of trade that are used to
calibrate the combined exposure and the derivative position.
Performance Evaluation
‡ The corporate risk management system must be evaluated
‡ Evaluation should assess the extent to which the overall goals have
been achieved-not whether specific transaction made a profit or loss.
‡ Risk managers can legitimately be evaluated in terms of how well
they manage the transaction costs of hedging, including the tax
payments that can arise out of employing derivatives.
‡ The manager should also act within a given budget, major deviations
from the budget should be explored and explained.
Chapter 3
Banking Regulation
ƒ There is little disagreement over the fact that banks are special entities and
require tight risk management standards and regulation.
ƒ After the near collapse of the world financial system following the 20072009 financial crisis and the fact that bank risk management have had a
huge influence on the more general world of financial risk management in
all sector economy have made this topic of global importance.
ƒ In this chapter we will take a global perspective and focus on the
successive waves of international banking standards devised by the Basel
Committee (Basel I, II and III).
ƒ We will look at how structural changes in the financial markets including
the internationalization of banking and dramatic growth of derivatives-led
to the key existing pieces of international bank regulation, the 1988 Basel
accord and its 1996 Amendment.
Bank Regulation and risk
activities, monitor their risk management
standards closely and impose a unique set of
minimum required regulatory on them.
ƒ Why do they do so?
ƒ There are two key reasons:
ƒ Banks collect deposits from ordinary savers,
and they play a key role in the payment and
credit system.
The push to standardized bank
capital management.
ƒ Prior to the implementation in 1992 of the 1988 Basel Accord,
bank capital was regulated in some countries by imposing
uniform minimum regulatory capital standards.
ƒ These are applied to banks regardless of their individual risk
ƒ Form the mid 1980, the Bank of England and the Federal
reserve Board become increasingly concerned about the
exposure of banks to off-balance sheet claims, coupled with
problem loan the third world countries.
ƒ The Federal Reserve Board and the Bank of
England assigned to the international Basel
Committee the job of studying the position
worldwide and proposing a set of common
procedures to the regulatory bodies.
ƒ The Basel Committee on Banking Supervision
( Basel Committee) has emerged as the nearest
thing the international banking industry has to
an international regulator,
The 1988 Basel Accord (Basel-I)
ƒ Represented the first internationally agreed capital
standard for banks.
ƒ Established international minimum capital guidelines
ƒ The accord was intended to raise capital ratios, which
were generally perceived too low.
ƒ It focused on credit risk which was perceived at that
time as the predominant risk factor in banking.
So what did the 1988 Accord
require of Banks?
ƒ It defines two minimum standards for meeting
acceptable capital adequacy requirements: asset to
capital multiple and a risk based capital ratio.
ƒ The Assets-to-Capital Multiple: it is calculated by
GLYLGLQJ WKH EDQN¶V WRWDO DVVHWV LQFOXGLQJ RII-balancesheet items, by total capital.
ƒ The maximum multiple allowed under Basel I is 20.
ƒ Risk based capital ratio: The second and more critical
measure takes the form of solvency ratio, known as the Cooke
ratio, that is defined as the ratio of capital to risk weighted onbalance-sheet assets plus off-balance-sheet exposures, where
the weights are assigned on the basis of counterparty credit
ƒ Capital and the Cooke Ratio: Banks are required to maintain
a capital amount equal to 8 percent of their total risk-weighted
ƒ Capital defined by the Cooke ratio includes both Tier 1 ( or
core capital) and Tier 2 ( or Supplementary capital) capital.
Why does Basel 1988 Need Replacing?
Or key Weakness of Basel I.
‡ The rules of original 1988 Accord are generally
acknowledged to be flawed for five reasons:
™ Assumes that a loan to a corporate counterparty generates
five times the amount of risk as does a loan to OECD banks.
™ Regulatory rules assume all corporate borrowers pose an
equal credit risk.
™ Does not take maturity factors into effect. Revolving credit
agreements with a term of less than one year do not require
regulatory capital.
™ Does not provide any incentive for using credit risk mitigation
™ Did not address complex issue such as portfolio effects.
Shortcomings produced a distorted assessment of actual risks
and have led to a misallocation of capital.
The Explosion of Bank Market Risk
and the 1996 Market risk amendment.
ƒ When devising the 1988 accord, regulators focused
primarily on the credit risks and ignored the market
risk and other risks.
ƒ Modern banks are engaged in a range of activities that
extend well beyond lending and credit risk that this
ƒ They trade all types of cash instruments, as well as
derivatives, such as swaps, forward contracts and
ƒ The new exposures of the banks need to be carefully
Group of Thirty (G30) Policy
‡ In1993, the Group of Thirty (G30) published a report
that listed 20 best-practice price risk management
recommendations for dealers and end-users of
¾ Group was comprised of end-users, dealers,
academics, accountants, and lawyers.
¾ Work mostly based on a survey.
¾ Focused on providing practical guidance in
managing derivative businesses.
Group of Thirty (G30) Policy
‡ G30 recommendations can be categorized into the
following groups:
¾ General policies
¾ Market risk policies
¾ Credit risk policies
¾ Enforceability policies
¾ Infrastructure policies
¾ Accounting policies
¾ Disclosure policies
The 1996 Market Risk
Amendment ( BIS 98)
ƒ The recommendations in G-30 report helped establish
qualitative standards for banks management of derivative
market risk.
ƒ But the explosion in bank trading of derivatives has forced the
regulators to rethink how to calculate the amount of regulatory
capital a bank should set a side to cover risk.
ƒ The 1996 Amendment to the 1998 accord, implemented in
1998, extended the initial to include risk-based capital
requirements for the market risk.
ƒ The amendment allowed sophisticated banks to use their own
internal VaR model to calculate regulatory capital for market
ƒ Under the amendment off-balance sheet derivatives, such as
swaps and options, were subject to both market risk charge and
the credit risk capital charges. However on-balance sheet
assets in the trading portfolio are subject to the market risk
capital charge only.
ƒ In addition to the market risk adequacy requirements, the
Basel committee set limits on concentration risk. Under the
must be reported.
ƒ Banks are forbidden to take positions that are greater than 25
BASEL II-A banking Revolution?
¾ In June 1999 the Basel Committee declared its intention to build
a new capital adequacy framework, known as Basel II to replace
1988 Accord.
¾ BIS 1999 objectives:
™ Promote safety and soundness in the financial system.
™ Enhance competitive equality.
™ Constitute a more comprehensive approach to risks.
™ Focus on internationally active banks.
¾ Basle Committee proposed a framework based on three
™ Minimum capital requirements.
™ Supervisory review process.
™ Market discipline as a lever.
The First Pillar of the Basel II AccordMinimum Capital Requirements
ƒ The Basel II framework maintained both the wide definition of
capital employed by Basel I and the minimum capital
requirement of 8 percent of risk-weighted assets. However, it
made two key changes.
ƒ First, besides the credit risk, the risk calculation extended to
include both market risk and operational risk:
ƒ Total Capital/( Credit risk + Market risk +Operational risk) = Capital Ratio
(Minimum 8%)
ƒ Where risk-weighted assets are the sum of the assets subject to market,
credit, and operational risk. Tier 2 capital cannot exceed 50 percent of total
regulatory capital, which is the sum of Tier1 and Tier 2 Capital.
The First Pillar of the Basel II AccordMinimum Capital Requirements
ƒ The second, key changes concerns the way that credit risk is to
be calculated. Banks are required to hold more capital for
high-risk borrowers relative to low risk-borrowers. To make
regulations sensitive to the varying degree of sophistication
among banking institutions, the regulator laid out three options
for calculation of the minimum required capital for credit risk.
1. The Standardized Approach: Under this approach, risk
weights are based on available external credit ratings. This
option was designed for banks engaged in less complex forms
of lending.
own internal ratings:
1. The IRB (internal-ratings-based) Foundation.
ƒ Under this approach to assessing the risk capital
requirements, banks will have to categorize bankingbook exposures into at least five broad classes of
assets with different underlying credit risk
characteristics: corporations, banks, sovereign, retail,
and equity.
2. The Internal Ratings Based(IRB) Advanced Approach: under
this advanced approach, banks can use their internal estimates of
borrower creditworthiness to assess the credit risk in their
portfolio, subject to the approval by the regulator. The key risk
parameters for calculating credit risk include the following:
Probability of default (PD) for each rating category
Loss given default(LGD)
Exposure at default(EAD) for loan commitments
Maturity of the facility(M)
ƒ A more sophisticated full modelling
ƒ A more comprehensive approach to risks,
which include bank operational risk, covering
a whole range of event risks such as computer
failures and fraud by staff, in their capital
The second pillar of the Basel II
Accord-Supervisory Review process
ensure that banks maintain adequate capital to
cover all critical risks, but also guide banks
towards increasingly robust internal risk
management systems.
ƒ The objective was to ensure that banks follow
rigorous processes, measure their risk exposure
correctly, and have enough capital to cover
their risk.
Four key principles of supervisory
ƒ Banks should have a process for assessing their
overall capital adequacy in relation to their risk
profile and a strategy for maintaining their capital
internal capital adequacy assessments and strategies,
as well as their ability to monitor and ensure their
compliance with regulatory capital ratio.
ƒ Supervisors should expect banks to operate
above the minimum regulatory capital ratios
and should have the ability to require banks to
hold capital in excess of the minimum.
ƒ Supervisors should seek to intervene at an
early stage to prevent capital falling below the
minimum required level to support the risk
characteristics of a particular bank.
The third Pillar of the Basel II
Accord-Market discipline
ƒ Market discipline serves to complement the requirements of
the other two pillars. The key features of this pillar is
ƒ This aims at supporting market discipline through enhanced
disclosure by banks in several areas, including the manner in
which a bank calculates its capital adequacy and its risk
assessment methods.
ƒ As per this accord buckets are now based on risk measures
rather than on types of assets. This would bring regulatory
capital for each exposure into closure alignment with the risk
of the underlying asset and encourage banks to adopt better
risk management practice.
The ± Post Crisis regulatory
Framework: Basel-III
ƒ The subprime crisis that erupted in July2007, and
which nearly led to a total collapse of the financial
system in the United States and other countries after
the bankruptcy of Lehman Brother in September
2008, prompted a major revision of bank regulation.
ƒ A series of fundamental reforms to Basel II were
introduced collectively known as Basel III.
Key Reforms
ƒ Some of the key reforms are as under:
ƒ A new tighter definition of capital, placing the emphasis firmly
on equity capital
ƒ Increased capital requirements and liquidity requirements
ƒ The coverage of additional risks in the minimum capital
requirement calculations ( e.g., counterparty risk for OTC
derivatives and repos transactions)
ƒ The introduction of a backstop leverage ratio in case the riskweighted calculations failed to capture bank risk.
ƒ Additional requirements for institutions
deemed to be systemically important
ƒ As series of measures intended to make sure
bank capital requirements did not act to
heighten economic cycles, including a new
countercyclical capital buffer.
Basel III: The key firm Specific
ƒ Basel III attempt to increase the amount and quality
funding and liquidity strategies.
ƒ Changes in the treatment of the three elements in the
capital equation are as under:
ƒ The Numerator: A Strict Definition of Capital
ƒ The Denominator: Enhanced Risk Coverage
ƒ Capital Ratio: Calibration of the new Requirements.
ƒ Liquidity ratios: The liquidity Coverage Ratio(LCR) and the
net Stable Funding Ratio (NSFR).
ƒ Basel III introduces an entirely new framework for managing
liquidity risk
ƒ The LCR requires that banks maintain high-quality liquid
assets sufficient to withstand a 30-day stressed funding
scenario specified by supervisors.
ƒ LCR = Stock of high-quality assets/Net cash outflows over the
next 30 calendar days
ƒ The LCR should be equal or greater than 100%
ƒ Where net cash outflows over the next 30 days = outflowsMinimum inflows(75% of outflows)
ƒ The LCR is complemented by the net stable funding
ratio(NSFR), which is a longer-term(one year)
structural ratio designed to address liquidity
mismatches and reduce reliance on the wholesale
funding that proved so unreliable during the crisis.
ƒ NSFR = Available amount of stable funding/required
amount of stable funding
ƒ The NSFR should be equal or greater than 100%
Basel III: A Systemwide, SystemicRisk-Based framework
intended to reduce systemic risk and lessen procyclicality-tendency for
bank lending to rise when times are good and tighten when times are
worse, thus worsening the economic cycle.
ƒ The macroprudential overlay consists of five elements.
1. Leverage Ratio = Tier I Capital/Exposure( $VVHWV EDQN¶V off-balance
sheet exposures +derivative exposure)
Banks will not be allowed to lower their leverage below 3 percent.
2. Countercyclical Capital Buffer: It is designed to protect the banking
sector from the losses resulting from period of excess credit growth
followed by a period of stress, and also to help and make sure that credit
remains available during this period of stress. It should be in range of 0 to
2.5 percent and should be held in tangible common equity.
3. Additional Loss-Absorbing Capital for Systemically
Important Financial Institutions(SIFIs)
4. Systemically important Markets and
Infrastructures(SIMIs): The case of OTC
5. Capture of Systemic Risk/Tail Events in Stress
Testing and Risk modelling
ƒ Banks tend to reinforce the momentum of underlying
economic cycles.
ƒ During an economic boom, banks tend to be excessively
health. Their lending, credit rating policies, risk measurement,
and provisioning practices begin to move in corelation with
HFRQRP¶V VKRUW-term business cycle.
ƒ The opposite is true during economic downturn. After 2008,
institutions that experienced extensive loss found it difficult to
replenish capital. This in turn, induced them to reduce lending
and dispose of assets in illiquid markets at fire-sale prices.
Their retrenchment triggered a weaking of economic activity,
thereby raising the risk of a further deterioration in the strength
of financial institutions.
ƒ The key challenge for the policy maker is countering
procyclicality while continuing to encourage banks to develop
risk- based decision-making process.
ƒ Basel III has tried to achieve the right balance by suggesting
number of ways.
The Theory of Risk and Return
‡ In this chapter, we will review five key theoretical models and
demonstrate how they relate both to one another and to the practice
of risk management.
1. Modern portfolio theory(MPT): The foundation of MPT was led
down by Harry Markowitz in 1952.
‡ Markowitz showed that rational investors select their investment
portfolio using two basic parameters: expected profit and risk.
‡ According to Markowitz, investors select financial assets for their
portfolio based on each asset’s contribution to the risk of a single
investment not in terms its own variance, but in terms of its
interaction with other assets in the portfolio.
‡ While it is true that the mitigation of risk may also lead to the
lowering of expected profits, if assets are selected carefully, then
diversification can allow investors to achieve a higher rate of return
for a given level of risk.
‡ To the extent that investors succeed in achieving this state, they arrive
at efficient frontier represented by curve solid line.
‡ The efficient frontier contains all portfolios of assets such that there
are no other portfolio that for a given amount of risk offer a higher
expected rate of return.
‡ Once a portfolio contains only assets that are on the efficient frontier,
it can be seen that a higher rate of return can be achieved only by
increasing the riskiness of portfolio.
‡ The lower part of the frontier, which contains all the inefficient assets
and portfolios, is represented by a dotted line.
The efficient frontier of Markowitz
2. The Capital Asset pricing Model(CAPM)
‡ Developed by William Sharp in 1960. This model showed that the risk of an
individual asset could be decomposed into two portions
‡ Risk that can be neutralized through diversification (diversifiable or specific
‡ Risk that cannot be eliminated through diversification( systematic risk)
‡ This conception allowed Sharp to define the premium that investors
demand for taking on the risk of market portfolio, as opposed to investing
in the risk-free asset.
‡ Market risk premium is simply the difference between the expected rate of
return on the risky market portfolio and the risk free-rate.
‡ Formula to calculate expected rate of return on individual asset is
‡ Expected rate of return on security = risk-free interest rate +beta x
(expected rate of return on market portfolio – risk-free interest rate)
‡ The CAPM model has become a key tool of financial economists in
understanding the behaviour that can be seen i


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