Literature Review On Portfolio Effects In Investing
Nearly all investors, whether institutional or individuals, seek to increase the future value of their assets or maximize their utility because a higher fund value gives them the ability to consume more. Investors wish to earn a return on their money. Cash has an opportunity cost: which is done by actually holding cash where by you fore go the chances to earn a good return on the investment. Furthermore, in an inflationary environment, the purchasing power of cash diminishes with high rates of inflation, bringing a rapid decline in purchasing power. In investments it is critical to distinguish between an expected return and a realized return. Investors invest for the future but when the investing period is over, they are left with their realized returns. What investors actually earn from their holdings may turn out to be more or less than what they expected to earn when they initiated the investment. The essence of the investment process: investors must always consider the risk involved in investing.
Investors would like high expected returns; however, their objective is subject to constraints, primarily risk though other constraints such as taxes, transaction costs and legal are facing all investors in the investment decision. The investment decision, therefore, must always be considered in terms of both risk and return. There are different types of risk. Risk is defined as the chance that the actual return on an investment will be different from its expected return. Within the realm of financial assets, investors can achieve any position on an expected return-risk trade-off. Investors unwilling to assume risk must be satisfied with the risk-free rate of return but if they wish to try to earn a higher rate of return, they must be willing to assume a higher risk. Since returns are somewhat predictable, investors can enhance their average returns by moving their assets around among broad categories of investments.
2.0 Literature Review
2.01 Portfolio Construction
The next investment decision requires determining an appropriate asset allocation for the portfolio. The construction of an appropriate portfolio involves asset allocation by determining the proportions of the investor�s wealth to put in each asset. Asset allocation is probably the important decision the investor will make and his or her decision affects both short and long-term investment performance of the securities selected. Asset allocation is a major determinant of the risk and future returns of diversified portfolios and the asset allocation of a diversified portfolio is considerably more important than the individual securities held. Security investment is risky and some asset classes have relatively little risk while others have considerable risk. The most difficult aspect of the asset allocation decision is to determine how to balance the fund�s need for long-term growth against the investor�s need to achieve investment results within shorter time frames.
Leibowitz and Krasker (1988) introduced a model to compare the investment performance of stocks and bonds.( William,1991) Both stock and bond returns are very volatile in Year 1 to 2 but the range of returns shrinks quite rapidly over time. In fact, there is a 36% chance that stocks will underperform bonds over a 5-year horizon and even a 24% chance over 20 years. (Charles,1998) The fact that stocks can greatly underperform in both the short and long term may cause many investors to seek a safer route than a 100% stock portfolio. Over a 1-year investment horizon, the choice between stocks and bonds reflects a standard risk-return trade-off. Over a 10-year horizon, the benefits of diversification start to emerge. (Martin L)
The mean-variance model of modern portfolio theory provides a rigorous approach for managing risk and return. Modern portfolio theory works best over short investment horizons and it may fail to address the concerns of investors with long-term investment horizons. As the investment horizon lengthens, the distribution of portfolio values becomes increasingly asymmetric and loses its value as complete measure of risk. To manage investment performance over planning horizons of 10 years or longer, we must sharpen our understanding of risk. Risk is decomposed into systematic and non-systematic risk. Non-systematic risk can be eliminated through diversification while systematic risk remains and cannot be diversified. To achieve a high expected return on investment while limiting risk exposure, an optimal asset mix will maximize the overall return while minimizing risk.
The optimal asset mix that maximizes overall return while minimizing risk depends on the assumed individual asset returns and their volatility over some extended period of time. Diversifying among multiple asset allocation may reduce risk while adding value to performance. Tactical asset allocation uses asset pricing models that forecast the relative returns of various asset categories and structure their portfolios so as to benefit from expected return differentials. The benefits of diversification among asset allocations are similar to the benefits of diversification among stocks and bonds. The expected return to the investor splitting their investment equally between two assets falls midway between the expected returns of the two asset portfolios. The risk borne by the investor nevertheless is lower than the midpoint between the risks of the two asset portfolios unless the returns of the portfolio are perfectly correlated.
Empirical evidence (Haim Levy,1981) shows that investors who invest completely with macroeconomic risk factor can expect a higher return with higher risk than an asset group without it. Investors who diversify among asset group that contain equal amounts of information reduces risk without reducing expected return as return is moved from one asset group with much information into the other asset group with little information. Investors should examine the available combinations of expected return and risk and choose a combination that gives the highest return according to risk preferences. The expected equity return will be different from period to period as the market�s information set changes over time. In short, transitory deviations of expected returns from mean returns are consistent with the time horizon and risk premiums. As economic conditions change, the investor�s attitude toward risk tolerance may change as well. Investors may be more risk-averse in periods of economic recession than in periods of economic expansion.(Edward C,1990) Moreover, a change in investor�s perception of future uncertainties in inflation or economic growth will certainly change desired returns.
2.01 Theories and Applications � Portfolio Effects investing in Apples & Pears
In the Perfect Portfolio Effect, an investor can choose to invest in apples, pear or both. In this particular situation, both apples have the desired negative correlation of -1, when one moves up on the market; the other acts reciprocal of the other. The examples below show the different return rates for both apples and pears. Although each fruit will potentially yield a return of 10%, it is in the best interest of the investor to diversify the risk in a variation of ways. The follow illustrations show the different combination of investments that can be made in relation to apples and pears.
50% of yielding 8% return and 50% of yielding 12% return
50% of yielding 6% return and 50% of yielding 14% return
Apple investment: ER= (0.5 *8%) + (0.5*12%) = 10 %
Pear investment: ER= (0.5* 6%) + (0.5* 14%) = 10%
In the above example, the risk of both Apples and Pears has not been decreased. Instead, the investor takes on the risks that are associated with market activity, i.e. inflation, decrease in demand etcetera and makes the decision to invest in only one asset. In either situation, the investor may yield more or less than the 8% for the first half of year for Apple and 12% for the second half of the year. The same theory applies to Pears. Keeping this in mind, the investor might want to invest in the following if they are a risk-averse investor.
Apple investment (0.5 *8%) + Pear investment (0.5* 6%) = 7%
If an investor classifies themselves as a risky investor, they would invest in the following based on the past historical activity of the particular asset.
Apple investment (0.5*12%) + Pear investment (0.5* 14%) = 13%
The last two situations illustrate alternative investment options the investor could entertain. In either situation, there are still risks associated with the investment. On the capital market, investors can on estimate the future returns of stocks based on historical performance measures and current market activity.
2.02 Modern Portfolio Theory
The original theory was developed by Markowitz in 1952 and focused on:
? Calculating risks
? Reducing risks
? Optimizing rate of returns for investors
According to the theory portfolio performance is determined by the following five determinants:
? Time horizon
? Risk tolerance
? Investment goals
? Financial means
? Level of investment experience(www.investopedia.com)
Modern Portfolio Theory (MPT) proposes how rational investors will use diversification to optimize their portfolios. According to MPT it is possible to construct an �efficient frontier� of optimal portfolios offering the maximum possible expected return for a given level of risk (R. Pike and B. Neale). There are four steps for portfolio construction:
? Security valuation
? Asset allocation
? Portfolio optimisation
? Performance measurement
MPT states that apart from looking at expected risk and return of one particular stock, investing in more stocks can give the benefit of diversification (�Not putting all your eggs in one basket�). Each stock has its standard deviation from the mean, called risk. Markowitz showed that investment is not just about picking stocks but about choosing right combination of stock. Markowitz identifies two kinds of risk:
? Market risk (=Systematic risk)
? Specific risk (=Unsystematic risk)
Risk is defined as �the uncertainty that you may not earn your expected return on your investment.�( www.partners.financenter.com) There is a distinction between market risks and specific risks. Market risks are risks that can not be diversified away, for example interest rates or recessions. Specific risk is a risk that is specific to individual stocks and can be diversified away as number of stocks in portfolio increases. There are eight types of risks as shown on the diagram below.
2.04 The Sharpe Ratio
�A risk-adjusted measure developed by William F. Sharpe, calculated using standard deviation and excess return to determine reward per unit of risk. The higher the Sharpe ratio, the better the funds historical risk-adjusted performance.�( www.investorwords.com) Efficient Frontier determines the most risk-efficient portfolios for a given collection of securities; Sharpe ratio goes beyond by helping to identify the best possible proportion of these securities to use in combination with a risk-free asset.
In mathematical terms, the quantity known as the Sharpe ratio represents a measure of the amount of additional return a portfolio provides compared to the linked risk.
It is defined as:
S(x) = (R � RF) / s(x)
Where x is some investment
R is the average annual rate of return
RF is the best available rate of return of a risk-free security
s is the standard deviation of R
2.05 Capital Asset Pricing Model
The Capital Asset Pricing Model was developed in 1964 by Sharpe; the theory is used to explain how efficient capital markets value securities by discounting future expected returns at risk-adjusted discounted rates.
Model explains how the capital market sets share prices and the importance of measuring risk and setting risk premiums to each asset. This model also explains the relationship between risk and the rate of return and is used in the pricing of securities. The following assumptions are made for this theory:
? All investors operate on a common single period planning horizon.
? All investors are rational and risk-averse.
? There are no transaction costs in trading securities.
? All securities are highly divisible.
? All investors select from investments by looking at expected return and risk.
? No one investor can influence the market price by their own transactions.
2.06 Security Valuation and Discount Rates
In order for a shareholder to receive a certain rate of return for their initial capital investment, a company must first assert a value to the stock being issued. Pike and Neale give a clear example of stock valuation which is illustrated below
Company X issues �1 mil shares for a 1 yr project offering a cash flow of �10 million at 25% discount rate:
V0 = �10m/(1.25) = �8m
Market price = �8m/�1m = �8/share
This example takes the company�s projected cash flow from the investment made (either in Debt or Equity) and issues a certain pound amount in shares made available on the capital market. A discount rate is added to the valuation of the stock in order to determine the percentage required return needed to convert the expected return into the present value. In other words, a discount rate is synonymous with an interest rate used to determine the present value of future cash flow.
2.07 Discount Rate- Three Major Components
The discount rate is the percentage required return used to convert future expected cash flows into their equivalent present values. The discount rate for an asset looks at three components, the allowance for risk, the allowance for time value of money and the allowance for price changes in the market. Theses allowances have been described in more detail below:
? Allowance for risk- the promised reward that provide and incentive for investors to expose capital to risk.
? Allowance for time value of money- compensation to investors for having to wait for their payments.
? Allowance for price changes- additional return required to compensate for the impact of inflation on the real value of capital.
The Capital Asset Pricing Model also makes the assumption that investors should be compensated in two ways: time value of money and risk. The following shows how the three allowances are expressed and results in a rate of return for the investor.
ra= rf + �a( rm- rf )
rf= Risk free rate (time value of money)
�a= Beta of the security
rm= Expected market return
2.08 Risk Free Rate
The risk free rate is properly defined as the time value of money and is represented by rf. Rf compensates the investors for placing money in any investment over a period of time. The amount of compensation will vary based on the length of time, the amount of the initial capital investment; the risk associated with the investment and external market influences. The latter part of the formula (�a( rm- rf) represents risk and calculates the amount of return needed for the investor to take on any additional risks. This is calculated by taking � (beta, which compares return of assets over a period of time) and compares it to the market premium (Rm-rf).
2.09 The Arbitrage Pricing Theory
The Arbitrage Pricing Theory was developed by Ross in 1976. This theory reviews the expected risk premium in relation to the expected market risk associated with the share. The act of arbitrage deals with taking profits for zero risk. In theory, this can occur when a portfolio�s expected risk premium is = 0. The risk premium relates to the additional return required from an investor who holds a risky investment. The equation below illustrates risks associated with the each asset. The risks factors refer to market activity like interest rate increase or decreases, changes in the inflation rate, currency risks and a list of other market risks.
ERj=Rf+ � 1(ERfactor1-Rf) + � 2(ERfactor2-Rf)+�+uj
? ERj= expected ROR on j
? ERfactor1=expected return on macro factor 1
? �1= the sensitivity of security j to factor 1
? uj= random deviation based on unique events affecting returns
The following bullet points are a list of assumptions associated with The Arbitrage Theory:
? ROR on share depends partly on macroeconomic factors and specific events in the company.
? Diversification can eliminate specific risk, leaving only market risk.
? Specifies the returns as a function of multiple macroeconomic factors that the market portfolio depends.
The limitations that are associated with the arbitrage theory are the fact that the theory only focuses on most influential factors that may affect returns (e.g. industrial production, inflation, personal consumption, money supply and interest rates). Although some specific risks are considered, they do not have as much importance as the market risk associated with the portfolio assets. Another limitation of the theory is that weighting have not been established for the market factors. The last limitation of this theory is that it sill in developmental stages and cannot be properly applied to diversifying one�s portfolio.
2.10 Risk and Return Calculations
One question that can be asked in reference to portfolio diversification is whether or not portfolio risk can be minimized through portfolio diversification? After properly researching the topic, it has been determine that risk can be minimized through choosing various assets that have negative correlations in order to mitigate the risks associated with each individual asset. In dealing with risk, diversification can significantly reduce specific risk associated with a company but cannot entirely eliminate market risks that derive from macroeconomic factors.
In measuring risk, it is imperative to keep in mind that the degree of correlation and weight of each asset is key to properly calculating risk. The following equation is a standard deviation equation and can be used to measure different potential capital investments of a firm. In terms of A and B, �A� can be denoted as Debt and �B� as Equity. In this situation, a company can determine the degree or weight of risk involved in either choosing to issue debt or issue equity and also determine the potential rate of return on either investment.
sp= v82 s2A + (1- 8)2 s2B +28(1-8)covAB
? 8= proportion of portfolio invested in A
? (1- 8)= proportion of portfolio invested in B
? sA2= variance of return on A
? sB2= variance of return on B
? covAB= covariance of returns from A & B (measures the relations between A&B)
2.11 Covariance and Correlation in Measuring Risk
As defined earlier in the key terms, the correlation describes how the each asset behaves in relation to one another. The correlation of AB is significant because it will show the investor or financial manager to what degree each asset (A and B) will relate to each other. Below is the formula for the correlation of A and B returns.
Correlation coefficient between A& B returns = rAB= covAB/ sA* sB
Below illustrates the formula for the covariance for A and B:
Covariance, covAB between A & B = covAB= S[pi(RA-ERA)(RB-ERB)]
Why do investors buy shares? Investors put capital into investments for the anticipated dividends and capital gains. In order to calculate the returns of for a shareholder, an equation can be applied.
Total Shareholder Return
t= any holding period
Rjt= % of return from shares
Djt= dividends per share
Pjt= share price
Rjt= Djt+ (Pjt-(Pjt-1) * 100
For example, if the share price of Company X in March 2005 is 209p and decreases to 120p in March 2006, the actual returns from the shares owned can be calculated to reflect the following:
Share price at the end of March 2005= 209p
Share price at the end of March 2006= 120p
Net dividend paid during 2005-2006= 5p per share
5p+ (120p-209p) *100=
=-84p * 100 = -40.2%
The above example illustrates how shareholders can lose a capital gain instead of earning dividends on the capital market. With any investment, there are still risk involved even after an investor employs risk mitigating tactics like diversification and using Theories and other financial experts and tools available.
2.12 Mean Variance Optimisation
The goal of the theory is to optimally invest funds in wide variety of assets. It is a quantitative tool, allowing making investment decisions by considering the trade-off between risk and return. There are single and multi period mean variance optimisers. Single-Period MVO considers designing of portfolio for single upcoming period and maximising return considering presumed level of risk. Multi-Period MVO is a strategy, rebalancing portfolio at the end of each period
2.13 Single Period Problem
? (www.effisols.com/basics/MVO.htm) Inputs:
o The expected return for each asset
o The standard deviation of each asset (a measure of risk)
o The correlation matrix between these assets
o The efficient frontier, i.e. the set of portfolios with expected return greater than any other with the same or lesser risk, and lesser risk than any other with the same or greater return.
2.14 Multi-period Problem
o The full historical data set
? Desired output:
o The Geometric Mean Frontier; i.e. the set of rebalanced portfolios with greater geometric mean return than any other with the same or lesser standard deviation, and lesser standard deviation than any other with the same or greater geometric mean return
2.15 The Markowitz Optimization Enigma
The MVO is recognised as the foundation, for the most modern portfolio diversification models. But majority of investors avoid using it. What is the reason for it? It is difficult to use compared with informal traditional ways, to which managers are used to. Also there are political reasons for not using it. Using MVO suggests significant changes in the structure of organisation and to the investment management processes. More quantitative investment processes should be developed within the company. To use MVO Company needs thoroughly knowledge of basic statistical concepts and modern portfolio theories. Experienced investors have experimented with MVO. They abandoned the effort when found their portfolios unintuitive and without obvious investment value. Those listed might be the most obvious answers for Markowitz Optimization Enigma.
2.16 Exact VS Approximate MV Optimizers
There are available two types of MV optimisers, Exact and Approximate. The differences are: processing time; entire frontier vs. single point solution; maximum size of the optimisation universe; and the ability to operate on standard personal computers.
Exact MVO assumes that it can find a solution for the entire efficient frontier. The drawbacks are relatively small universe size, long computing time and it dose not include transaction costs.
Approximate MVO is sufficient for large organisations and its computing abilities compared to latter is much faster. Limitation is that it calculates only one optimal portfolio near the efficient frontier as opposed to exact one.
According to Jauch & Glueck (1988), another reason why companies want to diversify is the fact that nowadays, technology and research leads to the development of new products. This can promise new revenue sources for the firm. Moreover, the reduction of risk may also be another motivation for unrelated diversification. The reliance on a single product line can stimulate a diversification move. For example, Hershey was almost a totally dependant on candy and confectionary business, a business that was vulnerable to the increased interest in health and health foods. Thus, it purchased Friendly ice cream, a chain of family restaurant based in Massachusetts and also the Skinner Macaroni company. The expectation is that Hershey�s nonconfection revenues will be about 30% of sales. In order to reduce risk, firms can enter business areas that are very stable so that the risks are dampened.
Another positive point that brings companies to diversify is that it sometimes can provide economies of scale. For example, two small firms may not be able to afford effective advertising programs which are expensive. But the combination of those two firms may give them a chance to do so and operate at an efficient level. Additionally, these two firms may afford to buy expensive automated heavy equipment which they need. Another reason of diversification is that companies will be able to exchange of skills and resources. This is very useful for many small companies. Skills or resources that can be imported and exported are usually associated with any functional are such as production, R&D, marketing skills, etc. Popular brand names can also be a reason for diversification. For example, Pillsbury bought Green Giant in part because Green Giant name and image would help Pillsbury introduce new food products.
Other than the reasons, we should also consider carefully about the types of risks in diversification. There are two types of risks, they are systematic risk and unsystematic risk. Systematic risk is �the risk which remains even after extensive diversification� (Bodie, Kane & Marcus, 2002). This is a risk that influences a large number of assets. An example is an economic crisis that struck the country. It is virtually impossible to protect investors against this type of risk. This systematic risk is also known as nondiversifyable risk. Whereas, unsystematic risk is sometimes referred to as a "specific risk". �It's risk that affects a very small number of assets. An example is news that affects a specific stock such as a sudden strike by employees.� (Investopedia.com, 2003). This unsystematic risk can be eliminated by diversification. It is also known as diversifiable risk
3.0 Framework and Data Analysis
The impact of Bonds , Currency, Oil and Gold on Portfolio Assets Stock
Data analysis and Findings
Model Variables Entered Variables Removed Method
1 portfolio, currency, bonds, info, oil , gold(a) . Enter
a All requested variables entered.
b Dependent Variable: sp
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .650(a) .422 -.040 .36542
a Predictors: (Constant),bonds, currency, info, oil, gold
MODEL SUM OF SQUARES DF MEAN SQUARES F SIG
.360 .345 .638a
conefficient t Sig
b Std.Error beta
Y=b0 + b1 X1 + b2 X2 + b3 X3 + b4X4 + error regarding SPSS sheet .
Y= 4.674 � 0.571 X2 - 0.502 X2 + 0.042 X3 + 0.36542
Portfolio Assets Stock = 4.674 � 0.571 (bonds) - 0.502 (currency) + 0.042 (oil) + 0.545 (gold) +0.36542
R= 0.65 there is almost 65% relationship between Portfolio Assets Stock and the four independent variables.
Significant value = 0.638, compare it with a=0.05
The value=0.064 more than a=0.05.
The relationship is insignificant.
Bonds value = 0.329, compare it with a=0.05
The value=0.329 more than a=0.05 the relationship is insignificant.
The relationship between Bonds and the Portfolio Assets was negative (-0.571), as hypothesized and it was not significant . H1 is not supported.
Currency value = 0.034, compare it with a=0.05
The value=0.034 less than a=0.05 the relationship is significant.
The relationship between Currency and the Portfolio Assets was negative (-0.502), as hypothesized and it was significant. H2 is supported.
Oil value = 0.036, compare it with a=0.05
The value=0.036 less than a=0.05 the relationship is significant.
The relationship between Oil and the Portfolio Assets was positive (0.042), as hypothesized and it was significant. H3 is supported.
Gold value = 0.047, compare it with a=0.05
The value=0.047 less than a=0.05 the relationship is significant.
The relationship between Gold and the Portfolio Assets was positive (0.545), as hypothesized and it was significant. H4 is supported.
It can be concluded that firstly, investors should use diversification to optimize their portfolios. Secondly, investors must keep in mind:
? The risk associated with each asset
? Correlation between assets within the portfolio and correctly weighing
Finally, risks can be minimized to a certain extent with the tool and theories mentioned in this report. But investors should be aware that some level of risk always remains. There are some risks that can be faced by a company during diversification. Some form of diversification can divert attention from main product. This actually damages the original business by diverting attention and resources from it. For example, Quaker Oats embarked on an aggressive acquisition program in the early 1970s, going into toys and theme restaurants. In the process, however, the company allowed its core business areas to deteriorate. Only one major new product was introduces in the U.S. market during 1970-1978, 100% Natural Cereal. The marketing program by measures such as share and shelf facings suffered (Sample case taken from Aaker, 1984). This type of diversification cost is often overlooked.
Another risk is management difficulties. According to Aaker (1984), a firm�s potential difficulties in managing diversification is magnified when an unrelated business is involved. Numerous firms have found they could not manage a diversification. The management team of the acquired firm might leave and are difficult to replace. The new business may be difficult to learn because the management skills and practices may be different from its previous or main business.
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