Modern Portfolio Theory: Definition, Problem and Solution

Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics.

MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has lower overall risk than any other combination of assets with the same expected return. This is possible, intuitively speaking, because different types of assets sometimes change in value in opposite directions For example, to the extent prices in the stock market move differently from prices in the bond market, a combination of both types of assets can in theory generate lower overall risk than either individually. Diversification can lower risk even if assets' returns are positively correlated.

More technically, MPT models an asset's return as a normally or elliptically distributed random variable, defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets, so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not perfectly positively correlated, MPT seeks to reduce the total variance of the portfolio return. MPT also assumes that investors are rational and markets are efficient.

MPT was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. Since then, some theoretical and practical criticisms have been leveled against it. These include evidence that financial returns do not follow a normal distribution or indeed any symmetric distribution, and that correlations between asset classes are not fixed but can vary depending on external events (especially in crises). Further, there remains evidence that investors are not rational and markets may not be efficient. Finally, the low volatility anomaly conflicts with CAPM's trade-off assumption of higher risk for higher return. It states that a portfolio consisting of low volatility equities (like blue chip stocks) reaps higher risk-adjusted returns than a portfolio with high volatility equities (like illiquid penny stocks). A study conducted by Myron Scholes, Michael Jensen, and Fischer Black in 1972 suggests that the relationship between return and beta might be flat or even negatively correlated.

Concept

The fundamental concept behind MPT is that the assets in an investment portfolio should not be selected merely individually, each on its own merits. Rather, it is important to consider how each asset might change in price relative to how every other asset in the portfolio might change in price.

Investing is a tradeoff between risk and expected return. In general, assets with higher expected returns are riskier. The stocks in an efficient portfolio are chosen depending on the investor's risk tolerance: an efficient portfolio is said to be having a combination[clarification needed] of at least two stocks above the minimum variance portfolio. For a given amount of risk, and on a lot of assumptions about the probability distribution of returns on each asset, MPT shows how to select a portfolio with the highest possible expected return. Or, for a given expected return, MPT explains how to select a portfolio with the lowest possible risk (the targeted expected return cannot be more than the highest-returning available security, of course, unless negative holdings of assets are possible.)

Therefore, MPT is a theory of diversification. Under certain assumptions and for specific quantitative definitions of risk and return, MPT explains how to find the best possible diversification strategy.

Example Problem and Solution:

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The Capital Assets Pricing Model

The Capital Assets Pricing Model

The capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset or equilibrium price of assets if that asset is to be added to an already well-diversified portfolio, given that assets non-diversifiable risk.

The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial literature, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Thus this is an extension of the work of Markowitz. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics.

Assumptions of CAPM:

1. All investors aim to maximize economic utility and they are rational and risk-averse meaning that they use the idea proposed by Markowitz.
2. Are broadly diversified across a range of investments.
3. All are price takers, i.e., they cannot influence prices.
4. Can lend and borrow unlimited amounts under the risk free rate of interest.
5. Trade without transaction or taxation costs.
6. Deal with securities that are all highly divisible into small parcels.
7. Assume all information is available at the same time to all investors.
8. Perfect Competitive Markets.

CAPM in Brief:

All investors will choose to hold a portfolio of risk assets in proportion that duplicates the market portfolio, which includes all traded assets. For simplicity we generally refer all risky assets as stocks. The proportion of each stock in the market portfolio equals the market value of the stocks. 

We consider that the market portfolio will not only be on the efficient frontier, but also in the tangency portfolio to the optimum capital allocation line [CAL] derived by each investors. As a result the CML [one of the CAL] will be the best capital allocation possible. As CML is the optimum one, therefore all investors will hold market portfolio differing only in the amount of investment.

Derivation in Simplest Form

Generally all the investors will hold Market Portfolio which is the tangency between CML and opportunity set. However, if we try to make a different strategy like: 

Market Portfolio: A market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market (with the necessary assumption that these assets are infinitely divisible).

Richard Roll's critique (1977) states that this is only a theoretical concept, as to create a market portfolio for investment purposes in practice would necessarily include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth, as the theoretical market being referred to would be the world market

Now, beta can be measured form the raw data as:

Period	Market HPR	Heidelberg Return
February 28, 2003	-0.084%	-0.37%
March 31, 2003	-6.950%	-7.35%
April 30, 2003	4.941%	9.33%
May 31, 2003	0.477%	0.18%
June 30, 2003	4.896%	0.72%
July 31, 2003	-3.670%	-1.98%
August 31, 2003	-0.858%	2.39%
September 30, 2003	-0.535%	0.72%
October 31, 2003	1.571%	0.89%
November 30, 2003	14.894%	20.11%
December 31, 2003	5.135%	-2.06%
January 31, 2004	-0.692%	-1.65%
February 29, 2004	-0.767%	-0.76%
March 31, 2004	2.104%	2.30%
April 30, 2004	14.202%	9.76%
May 31, 2004	6.621%	2.33%
June 30, 2004	11.223%	6.15%
July 31, 2004	-2.258%	-8.31%
August 31, 2004	17.388%	20.88%
September 30, 2004	7.912%	4.43%
October 31, 2004	4.742%	-9.58%
November 30, 2004	9.740%	4.45%
December 31, 2004	5.022%	8.76%
	Beta	0.967479052

The Value of Beta:

The value of beta can be any positive value or any negative value. However absolute value of beta has different meaning to the investors.

§  A higher beta means that the sensitivity of the security return with the market return is very high. Therefore it is mot likely to be a risky security. However if the value is positive then, the security will give higher return if the market return goes up and vice-versa. Moreover a security with higher beta will be considered as aggressive stock.

§  A lower beta [lower than 1] means that the sensitivity of the security return with the market return is very low. Therefore it is mot likely to be a less risky security. However if the value is negative then, the security return will go down if the market return goes up and vice-versa. Moreover, a security with lower beta will be considered as defensive stock.

§  The Beta of 1: This is the beta of market portfolio. Because theoretically the sensitivity of market returns with market return is 1. Therefore we consider that market beta is always 1. Alternatively since some security will be aggressive, some will be defensive, some will be more aggressive or defensive, some will be less aggressive or defensive, therefore sum of all of them in one portfolio, which is market portfolio, will be 1.

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed. If an asset is undervalued by CAPM it should be bought and an overvalued by CAPM then it should be sold.

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Case Study on Claim Settlement: Corporate Blanket Cover for Foreign Travel Insurance

Topic: This case study is on Corporate Blanket Cover for Foreign travel

This case study contains three parties:

1. Insurance Company: Bajaj Allianz
2. Insured Company: Honeywell
3. Service Provider Company: International SOS

Insurance Company: Bajaj Allianz General Insurance Company Limited is a joint venture between Bajaj Finserv Limited (recently demerged from Bajaj Auto Limited) and Allianz SE. Bajaj Allianz today has a countrywide network connected through the latest technology for quick communication and response in over 200 towns. 

Insured Company: Honeywell is a Fortune 100 company that invents and manufactures technologies to address some of the world’s toughest challenges linked to global macro trends such as energy efficiency, clean energy generation, safety and security, globalization and customer productivity. With approximately 132,000 employees worldwide, including more than 22,000 engineers and scientists. Its business units are on Aerospace, Automation and Control Solutions, Performance Materials and Technologies, Transportation Systems etc.

Service Provider Company: International SOS is the world’s leading medical and travel security Services Company. They help organizations to protect their people across the globe. Their teams work night and day from more than 700 locations in 76 countries. International SOS started its operations in India in 1998. We employ over 200 full-time staff and operate out of three offices in Bangalore, New Delhi and Mumbai.

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About the incidence:

1.     Five Employees of Honeywell were on an assignment at Phoenix in US.

2.     They were returning in a Car on 14/06/03 and at 19.30, and their car was hit by another car.

3.     It was a tragedy that two people sitting the rear seat namely Mr.  Sunil Siddeswara Swamy and Mr. Shastri Ajit Hosudi were badly injured. They were immediately admitted in a hospital and expired the same day in the Hospital.

Some facts about the Travel Insurance Policy:

1.     Travel insurance is insurance that is intended to cover medical expenses, financial default of travel suppliers, and other losses incurred while traveling

2.     It is either within one's own country, or internationally.

3.     Temporary travel insurance can usually be arranged at the time of the booking of a trip to cover exactly the duration of that trip, or a "multi-trip" policy can cover an unlimited number of trips within a set time frame.

4.      Coverage varies, and can be purchased to include higher risk items such as "winter sports".

Bajaj’s Travel Insurance Policy:

1.     Bajaj’s corporate travel insurance plan is a comprehensive package which provides complete medical and health cover to the international business traveler.

2.     Bajaj’s corporate travel insurance plan covers business trips abroad.

3.     They offer customized plans for virtually every requirement of corporate employees traveling abroad.

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Their plan as follows:

Covers	Corporate Lite Benefits (USD)	Corporate Plus Benefits (USD)
Medical Expenses, Evacuation and Repatriation	250,000	500,000
Emergency dental pain relief included in (I) above	500	500
Loss of Baggage (Checked) Note: Per Baggage maximum 50 % and per item in the baggage maximum 10 %.	1,000	1,000
Delay of Baggage	100	100
Personal Accident	15,000	30,000
Loss of Passport	250	250
Personal Liability	2,00,000	2,00,000
Hospitalization Daily Allowance	$25 per day to max $150	$25 per day to max $150
Hijack	$50 per day to maximum $ 300	$50 per day to maximum $ 300
Trip Delay	$ 20 per 12 hrs to max $ 100	$ 20 per 12 hrs to max $ 100
Total Coverage During the Year Maximum	180 days	180 days
Per Trip Duration	45 days	45 days

This plan covers:

1.     Covers expenses of hospitalization, loss of baggage and other incidental expenses

2.     Covers against trip cancellation, trip curtailment and burglary of home

3.     Quick disbursement of claims

4.     Global expertise matched with local knowledge

5.     Innovative packages to match individual needs

6.     Only insurance company with in-house international toll-free numbers and fax numbers

Here the case contains the facts:

1.     Destination: Phoenix in US

2.     Feature: Personal Accident

Information Processing:

The CFO of Honeywell, Mr. Ramanathan called the Bangalore RM, Mr.  J. K. Bhagat around 15.30 IST on 15/06/03. Immediately the Bangalore office informed Bajaj’s worldwide Travel Insurance Service Provider - International   SOS   Private Limited at Delhi. They sought the details from their office in Philadelphia, who got in touch with Honeywell Project Manager and obtained the details of Accident. They reverted to us confirming the demise of the two Honeywell employees. A conformation of the coverage provided to them was informed to International SOS and Bajaj’s office requested them to extend all possible assistance to Honeywell.

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Claim settlement procedure:

Bajaj settled the Personal Accident claims of both the employees on 18.06.03 for Rs.23, 38,500.00 (Equivalent to USD 50,000) and handed over the Pay order on the same day. The time taken for settlement was 4 days flat from the date of claim intimation and the unfortunate incident.

Now I will state the procedure of claim As per Bajaj’s requirement

Steps:

Step 1: Complete online or mail-in (fax) claim notification form.

Step 2: Complete with great attention to detail, downloaded or received in the mail claims forms. Follow guidelines as to which documentation is required by Travel Insured in processing your claim. If proper support documentation is not received your claim will be held up and the entire process becomes arduous.

Step 3: You will be required to submit proof of payment (canceled bank check) and copies of travel documents (airline tickets, day by day travel program given to you by Select International Tours & Cruises), a doctor's note clearly stating why you are unable to travel and when if due to medical reasons, etc.

Step 4: You will need to submit a refund statement from Select International Tours & Cruises stating how much of your payment is non-refundable.

Step 5: Additional Medical Documentation may be required and you will be notified by us if that is the case.

Step 6: You may need to complete "Excess Medical Expense" form along with an accompanying "Explanation of Benefits" from your health insurance company. The purpose of this document is to make sure your primary medical coverage from your health insurer and your secondary medical coverage from Travel Insured are coordinated.

Step 7: A Travel Insured claims examiner will review your documents and resolve your claim once all the required documentation is submitted by you. The claim process takes us up to 12 weeks, however it can be substantially faster if you provide all the needed documentation and the paperwork is completed properly.

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Extra Assistance of Bajaj Allianz to Honeywell:

Meanwhile the client requested us for early repatriation of the mortal remains and also to route them through Bangalore Customs, to avoid unnecessary hardship to the bereaved families. The Bajaj Allianz office acted very fast and ensured that the mortal remains reached Bangalore by 22/06/03. Bajaj Allianz had also taken extreme care in arranging for hassle-free autopsy, embalming   of the bodies, packing them in coffins in perfect manner through the service provider, who have commissioned Undertakers both in US as well as in Bangalore, to handle all formalities. The service provider also organized cancellation of passport of the deceased as well as obtaining required documentation for bringing in the mortal remains. The air tickets for the relatives accompanying the mortal remains, though the request was made to Bajaj Allianz at the last moment by Honeywell, were also arranged. In order to fulfill Honeywell's request for receiving the mortal remains through Bangalore Customs, Bajaj Allianz had to reschedule the travel arrangements for a Lufthansa flight, which lands at Bangalore directly.

Findings:Bajaj Allianz could speedily settle the claim because of the close co-ordination between the client and service provider. A constant six hourly updates was shared between the HO, Bangalore office, client and their US office and the service provider. They acted fast and offer their best they can do.

Foreign Travel Policy in Bangladesh:

There are several companies that offer foreign travel insurances. It contains:

1. Comprehensive Travel Insurance
2.  Overseas Medical Insurance (accident or sickness)
3. Personal Accident Insurance
4.  Loss of Baggage insurance
5. Emergency evacuation
6. Repatriation of remains
7.  Return of a minor
8. Trip cancellation
9. Trip interruption
10. Visitor health insurance
11. Accidental death, injury or disablement benefit
12. Overseas funeral expenses
13.  Lost, stolen or damaged baggage, personal effects or travel documents
14. Delayed baggage (and emergency replacement of essential items)
15.  Flight connection was missed due to airline schedule
16. Travel delays due to weather
17. Hi-jacking etc.

References:

1.     http://www.bajajallianz.com/Corp/index.jsp

2.     http://en.wikipedia.org/wiki/Travel_insurance

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