Portfolio management

Portfolio management

Portfolio management refers to the management of the company’s capital structure by applying
different combination of how a company invests its finances by combining equity or debts or a
hybrid of the two or by a combination of securities. The proportion of a company’s long-term,
short-term debts and its dividend policy determines its investments options. The capital structure
and its management affect the company’s financial risks and the value of the company. The
theories in portfolio management and the capital structures assist in understanding the
relationship that exists directly between the value of the firm and the composition of its capital
structure. Weighted average cost of capital is actually the marginal cost of raising extra or
additional capital and is generally affected by costs of capital involved and the relative
proportion of each source of capital. These paper attempts to analyze different portfolio
management strategies that involve the Mean variance optimization and the Modern Portfolio
Theory while utilizing the single or multi period strategies also it looks at the MVO products, the
Mvoplus or the VisualMvo for investment evaluation.
Introduction
The major objective of the portfolio management theory is to optimize the allocation of funds to
portfolios that will result in maximum returns to the investors. The Mean Variance Optimization
is statistical quantitative tool that allows allocation of funds by putting into consideration the
trade off that exists between the risk and the assets return. The single period qualitative tool was
developed by Markowitz (1991).

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The multi period MVO strategy major objective is to maximize the real multi-period earnings for
a particular given level of the firm’s fluctuation. The MVO multi- period analysis is concerned
with specific strategies where the portfolio is rebalanced to a particular specified allocation
which results at the end the period. These strategies are the Constant ratio asset allocation or the
Constant proportions. (Bernstein & Wilkinson, 1997)
1.2. a) The investment objective of a company is to meet the anticipated long and short-term
financial requirements of the company within the acceptable risk tolerance range of each
designated fund. The investment objective also provides a reasonable basis for the analysis of the
performance of the portfolios by the various section managers and evaluating their fiduciary
responsibility towards investment supervision.

Investments

  Minimum Target Maximum
Fixed Income 20% 20% 20%
Equities 0 0 0
Cash &
Equivalents

20,000,000 20,000,000 20,00,000

The investment policies of the company are used to communicate clearly the stated objectives,
performance standards and the general guidelines to the investment managers and individual
advisors. The main objective of the investment policy is to preserve the capital and moderate the
firm’s growth and offer secure liquidity with minimum risk exposure. It also targets investment
optimization of returns that are within the firms constraints.

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The constraints outlaws certain investments like the floating rates whose maturities are two years
or less that contain reset features like caps and floors. Also Swaps, derivatives and all forms of
equities.
The constraint also defines the allowed investments like the government backed securities,
commercial papers, convertible bonds and high yields bonds. The cash and cash equivalents are
made up of commercial papers and investment in government securities.
1.2. b). The portfolio structure has been diversifying to prevent over reliance on one particular
stock. This has been done in order to reduce the risk that is normally associated with investing in
one particular type of stock. In case of unforeseen circumstances like companies going under
after financial crisis then the losses will be minimized. (Levinson, 2006)
The CAPM model indicates that the cost of capital for an investment when diversified is lower
and the investor holds overall market portfolio minus the provision for the contribution to the
reduced risk which is measured by the market beta. Projects with a higher market beta must have
a return with higher and better expected rate of return for it to be marketable.
This assumption of the CAPM model is one of the major reasons for its weaknesses. From the
Empirical studies carried out by Black, Jensen and Scholes indicate that stocks with low betas
can also have high returns. (Black, Jensen and Scholes, 1972)
1.2c) The characteristic of the commercial paper and the government securities is that their
returns are guaranteed and they can easily be converted into cash. The portfolio has been
selectively balanced to minimize the overall probability of very low negative returns which has
been defined as negative 5% in one year. It’s also anticipated but not really guaranteed that a loss
greater than negative 5% will occur in the next twenty years. The ever changing economic

4 Finance – Portfolio Management
conditions both micro and macro may have some effect on the valuation of the short term
securities and also bonds but the long term effects are very favorable.

2.1) Alpha indicates the excess earnings generated over the expectations of the CAPM while beta
expresses its volatility as compared to the whole market.
Ɋa = Ra – ( Rf +βa (Rm – Rf))
Ɋa = Alpha of Asset A
Ra = Return of Asset A
Rf = Risk Free Rate
βa = Beta of the asset
Rm = Return of the market
The risk free rate has been taken from the 13- week Treasury bill rate and it’s averaged as 4%.
The beta has been taken as 0.34 the current coca cola beta and the NASDAQ current market rate
is 20.07%. The return on the asset has been taken as 18%
Ɋa = Ra – (Rf +βa (Rm – Rf))
Alpha = 18 – (4 + 0.34 (20 -4)
Alpha = 8.56%

Asset Class Strategic
Asset

Tactical
Asset

Performance
  Allocation Allocation Benchmark

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Fixed income 20% 15 – 45% Coca Cola Aggregate
       
Cash and cash
Equivalent

20% 0 – 20% Citigroup 3 month T- Bill

An asset that has a beta of 1is expected to earn more than the average market while an asset with
a beta that’s less than 1 should earn less than the average market.
Sharpe measure = total portfolio return – risk free rate/ portfolio standard deviation
The standard deviation of the whole market has been assumed to be 7
Sharpe measure = total portfolio return – risk free rate of return / portfolio standard deviation
Sharpe ratio = 18 – 4 / 7 = 2
Treynor uses the same formula only that beta is used in the place of standard deviation.
Treynor = 18-4 / 0.34 = .14/.34 = 0.41
The Treynor indicates that stock A achieved more returns than each unit of risk.
The Sortino ratio basically uses the same formula as the Sharpe ratio,
Total portfolio return – risk free rate of return/ portfolio standard deviation (down side only)
2.2) One of the basic principles of finance is that the higher the risk an asset has the higher the
return. Investors are mostly willing to venture into risky investments as long as the returns
measure up to the degree of risks involved. However, most investors target very high returns
with minimum risks. Several measures can be applied to measure the risks involved in an
investment. Jensen’s alpha is arrived at by taking the existing or the current portfolio earnings

6 Finance – Portfolio Management
and subtracting the expected earnings or returns according to the Capital Asset Pricing Model.
(CAPM) The CAPM calculates the expected asset return based on the beta, risk free rate of
interest and the market’s average return. Alpha indicates the excess earnings generated over the
expectations of the CAPM while beta expresses its volatility as compared to the whole market.
Ɋa = Ra – ( Rf +βa (Rm – Rf))
Ɋa = Alpha of Asset A
Ra = Return of Asset A
Rf = Risk Free Rate
βa = Beta of the asset
Rm = Return of the market
The risk free rate has been taken from the 13- week Treasury bill rate and it’s averaged as 4%.
The beta has been taken as 0.34 the current coca cola beta and the NASDAQ current market rate
is 20.07%. The return on the asset has been taken as 18%
Ɋa = Ra – (Rf +βa (Rm – Rf))
Alpha = 18 – (4 + 0.34 (20 -4)
Alpha = 8.56%

Asset Class Strategic
Asset

Tactical
Asset

Performance
  Allocation Allocation Benchmark
Fixed income 20% 15 – 45% Coca Cola Aggregate
       
Cash and cash 20% 0 – 20% Citigroup 3 month T- Bill

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Equivalent

An asset that has a beta of 1is expected to earn more than the average market while an asset with
a beta that’s less than 1 should earn less than the average market.
Sharpe measure = total portfolio return – risk free rate/ portfolio standard deviation
The standard deviation has been assumed to be 8.
Sharpe measure = total portfolio return – risk free rate of return / portfolio standard deviation
Sharpe ratio = 18 – 4 / 8 = 1.75
Treynor uses the same formula only that beta is used in the place of standard deviation.
Treynor = 18-4 / 0.34 = .14/.34 = 0.41
The Treynor indicates that stock A achieved more returns than each unit of risk.
The Sortino ratio basically uses the same formula as the Sharpe ratio,
Total portfolio return – risk free rate of return/ portfolio standard deviation (down side only)
Performance Attribution is a technique that analyzes the reasons why portfolio’s performance
and the bench mark differs. This method compares and analyzes the total return of the actual
investment with the actual return for a specific benchmark portfolio the difference is
decomposed into a particular selection and allocation effect.
.
3.1
Total cash invested 100,000,000
Asset Class Bench Asset stock interaction total Portfolio Portfolio Bench

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mark active mark
return allocation selection weight return weight
Fixed income 3.00% 0.60% 1.40% 0.40% 2.40% 90% 5.00% 70%
Cash & Cash equiv 1.00% -0.20% 0.00% 0.00% -0.20% 10% 1.00% 30%
Total 2.40% 0.40% 1.40% 0.40% 2.20% 100% 4.60% 100%

3.2
3.3. Bond immunization is a strategy in investment that minimizes the bond investment rate of
interest risk by adjusting and marching the portfolio duration to the investor’s investment time.
Immunization locks a particular fixed rate of return at a time when the investor keeps the bond
without actually cashing it. Bond prices are affected inversely by interest rates. When the
interest rates
raise the bond prices decrease. But when they are immunized, the investor receives a certain rate
of return for a specified period regardless whether the interest are increasing or decreasing. The
bond is actually immune to fluctuation in interest rates.
The duration of the bonds must be known before the bond can be immunized.

4.4 Derivatives are financial instruments whose values are basically derived from the real value
of the underlying security. The examples include call and put options which offer the holder the
right to buy or sell respectively the securities at strike price. Future contracts are contracts that
are financial in nature and obligate the buyer or the seller to either sell or buy assets in the
financial contract at the future date that has been specified.
Eurex Bonds Hedge Ratios valid from December 23 rd , 2013
Basis for March 2014 – Deliverables

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The bonds were dated 23 rd December and were identified as FGB-H4Z301 DE009689133
FGBB031/14-SCHATZ and rated 11, 12 and 15%. The conversion factor is 0.902732 with a
Hedge Ratio of 9.03 and future sizes of 9 for bonds that are less than one million. The Amount is
€ 1,000,000 and the term is 2 years. www.eurexchange.com
For the asset manager to fully hedge the interest rates and the associated risks of by applying the
bond futures. The formula would be HR = ∆Pa/ ∆Pf ×βaf. (Burghardt, Belton, Lane and Papa,
2005)
Where
HR = The hedge ratio
∆Pa = Price change as a result of the percentage change in the future contract par value in
response to the change in the prevailing interest rate.
βaf = Average change in the rate of interest for the hedged asset in response to the change of
interest for the future contract. When the ∆Pa/ ∆Pf is higher then the HR value is also higher.
∆Pf = Price change as a result of the percentage change in response to the change in the
prevailing interest rate. This is 1.5 % i.e. the average change between 11, 12 and 15% as
provided for under the Schatz. www.eurexchange.com
To calculate the number of contracts, the hedge ratio is multiplied by the face value of the bonds
and then the results are divided by the future contracts value. (Krgin, 2002)
Contracts = HR * PVa/PVf
HR = Hedge ratio (9.03)

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PVa = Face value of the asset (1,000,000)
PVf = Face value of the bond futures (11,500) i.e. 1.5% of 1000,000.
Bond future contracts = 9.03* 1000000/11500 = 785.22
The asset manager needs to sell 785 bond futures.
The asset managers of various institutions apply several kinds of hedging strategies that involve
future and forward markets that eventually reduces the market interest rates risks. This is
normally done by hedging the risks in interest rates on the invested treasury bonds.
Foreign currency options basically known as options are contracts that involve upfront fees and
which entitle the owner not to trade but to retain a specified quantity of foreign currency at
specific price and over a certain period. There are several variations of options that are available
i.e. the puts and the calls, the American, European and future styles. The major difference
between options and the other forms of hedging is that options are non – linear. (Albuquerque,
2007)
In corporate finance such as banks, pension funds, insurance and mutual funds they utilize two
basic types of hedging strategies that mostly involve the forward and future markets that reduces
the interest rate risk. When a financial company hedges risks of interest rates for a specified asset
its known as micro hedging while if it applies to the general portfolio it’s referred to as macro
hedging. (Hagelin and Pramborg, 2004)
For example, if the First American bank has 10% treasury bonds with $10 m face value that’s
currently selling at par and matures in the year 2022 (Current date is March the year 2012)
Fluctuations in the rates of interest causes major fluctuations in prices that may result in capital

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gains or losses. One method of hedging prices of stock or long term bonds against risks with
forward contract that’s a written contract that specifically specifies the price that it will buy or
sell that particular currency at a specified future date. The First American Bank may agree to sell
the stock at the current market price and at the rate of interest i.e. at $10m 10% bond one year in
advance to another company in future. (Hagelin and Pramborg, 2004)
Future options are utilized to offset risks that are created when financial institutions extend or
give out option like or stock commitments to certain customers. Banks can offer fixed rate loans
or stock commitments to their clients that would allow the customers to borrow at their own
discretion unto a specified amount given the option that allows them to sell the stock or bond to
the bank at a particular rate of interest.
4.5) An investment strategy is considered as market-neutral that seeks to minimize the market
risks totally like hedging. The risks have to be identified in order to analyze market neutrality. A
portfolio that is real market neutral shows signs of zero correlation with sources of risks that are
unwanted. Examples of hedging are;
In corporate finance such as banks, pension funds, insurance and mutual funds they utilize two
basic types of hedging strategies that mostly involve the forward and future markets that reduces
the interest rate risk. When a financial company hedges risks of interest rates for a specified asset
its known as micro hedging while if it applies to the general portfolio it’s referred to as macro
hedging. (Hagelin and Pramborg, 2004)
For example, if the First American bank has 10% treasury bonds with $10 m face value that’s
currently selling at par and matures in the year 2022 (Current date is March the year 2012)
Fluctuations in the rates of interest causes major fluctuations in prices that may result in capital

12 Finance – Portfolio Management
gains or losses. One method of hedging prices of stock or long term bonds against risks with
forward contract which is a written contract that specifically specifies the price that it will in
future buy or sell that particular currency at a specified future date. The First American Bank
may agree to sell the stock at the current market price and at the rate of interest i.e. at $10m 10%
bond one year in advance to another company in future.

13 Finance – Portfolio Management

References
Hull, J (1989). Options, Futures and Other Derivatives. . Upper Saddle River, New Jersey
Pearson
Prentice Hall.
.
. Deventer, D., Imai, K., Mesler, M. (2004). Advanced Financial Risk Management, An
Integrated Approach to Credit Risk and Interest Rate Risk Management. John Wiley & Sons
Sullivan , Sheffrin, S (2003). Economics: Principles in action. Upper Saddle River, New Jersey
Pearson, Prentice Hall.
http://research.stlouisfed.org/publications/iet/
Homer, S, Sylla, R., Sylla, E (1996), A History of Interest Rates , Rutgers University Pre ss.

Markowitz, H.M., (1991) Portfolio Selection, second edition, Blackwell.
Bernstein, W.J. & Wilkinson, D. (1997) Diversification, Rebalancing and the Geometric Mean
Frontier , research manuscript.

Vance, D. (2003) Financial analysis and decision making: tools and techniques to solve
financial problems and make effective business decisions. New York: McGraw-Hill.
Tofallis, C. (2008). “Investment Volatility: A Critique of Standard Beta Estimation and a Simple
Way Forward”. European Journal of Operational Research 187
Klarman, S., Williams, J. (1991). “Beta” Journal of Financial Economics 5 (3): 117.

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Doi : 10.1016/0304-405X (77)90041-1 .
Levinson, M. (2006). Guide to Financial Markets. London: The Economist (Profile Books).
pp. 155–6. ISBN   1-86197-956-8
Scholes, M., Williams, J. (1977). “Estimating betas from nonsynchronous data”.
Journal of Financial Economics 5 (3): 309–327.
http://us.spindices.com/indices/equity/sp-asx-100
Arnold, G. (2005). Corporate financial management (3. ed. Ed.). Harlow [u.a.]: Financial
Times/Prentice Hall. p. 354.
Black, F., Jensen, M. and Scholes, M (1972). The Capital Asset Pricing Model: Some Empirical
Tests, pp. 79–121 in M. Jensen ed., Studies in the Theory of Capital Markets. New York:
Praeger Publishers.
Bodie, Z., Kane, A., Marcus, A. J. (2008). Investments (7th International Ed). Boston: McGraw-
Hill. p.303.
Chong, J., Yanbo, J., Phillips, M. (2013). “The Entrepreneur’s Cost of Capital: Incorporating
Downside Risk in the Buildup Method” . Retrieved 25 June 2013.
Fama, E. F., French, K. R. (2004). “The Capital Asset Pricing Model: Theory and Evidence”.
Journal of Economic Perspectives 18 (3): 25–46.
Luenberger, D. (1997). Investment Science. Oxford University Press.
Mehrling, Perry (2005). Fischer Black and the revolutionary Idea of Finance. Hoboken: John
Wiley & Sons, Inc.

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Mullins, David W. (1982).Does the capital asset pricing model work? Harvard Business Review,
January – February 1982, 105-113.
Albuquerque, R. (2007) Optimal Currency Hedging, Global Finance Journal, 18 (1), 16- 33.
Hagelin, N. and Pramborg, P (2004) Hedging Foreign Exchange Exposure: Risk Reduction from
Transaction and Translation Hedging, Journal of international Management and Accounting, 15
(1)
Burghardt, G., Belton, T., Lane, M. and Papa, J. (2005) The Treasury Bond Basis. New York,
NY: McGraw-Hill.

Krgin, D. (2002) Handbook of Global Fixed Income Calculations. New York, NY: John Wiley &
Sons.