Strategic Asset Allocation and International CAPM

Contents

1 Introduction
1.1 Goal of the paper and problem setting
1.2 Methodology

2 International Capital Asset Pricing Model
2.1 The model and assumptions
2.2 Diversifying internationally and the weaknesses of the model
2.3 The model of time varying returns in the International Capital Asset Pricing Model

3 Currency Hedging
3.1 The rate of hedged asset classes
3.2 Time horizon and mean reversion
3.3 Tradeoff between risk and return under consideration of hedging strategies
3.4 Black’s Universal Hedging Implications for currency hedging

4 Asset Allocation and Portfolio Choice
4.1 Forms of Asset Allocation
4.2 Risk, return and investment horizon
4.3 Principles and decision points in Strategic Asset Allocation
4.4 Inflation indexed bonds as an alternative investment
4.5 Strategic Asset Allocation under consideration of VaR principles
4.6 Mutual fund theorem and upcoming mean reverting

5 Conclusion

References

List of abbreviations

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1 Introduction

1.1 Goal of the paper and problem setting

The decision as to which Assets should be included in a portfolio is first addressed in a Strategic Asset Allocation policy.

The determination of the Strategic Asset Allocation is one of the most important factors that influences a portfolio’s performance.

The process of defining a policy within the Strategic Asset Allocation should be done by both the portfolio manager and the potential investor.

Together with the International Capital Asset Pricing Model the Strategic Asset Allocation tries to find an optimal portfolio which maximizes return and, at the same time, tries to minimize the possible risk. Due to currency and inflation risk, hedging should be considered as crucial point during the Strategic Asset Allocation.^{[1] [2]}

Strategic Asset Allocation under consideration of the International Capital Asset Pricing Model decides to which asset classes a portfolio should be divided. Factors which determine the decision are expected returns, variances and covariances as well as the degree of risk aversion.

The analysis of mean-variance which was mostly developed by Harry Markowitz gave portfolio advice until the early eighties concerning the optimal asset allocation.

The aims of this approach were to minimize risk while receiving the highest possible return. Over the years the method was critized several times because of a lack of decisive factors. Markowitz only assumed a one period model and permanent income, currency and inflation risk were also ignored.^[3] Strategic Asset Allocation is much more than investing short- term. Investors care about inflation and currency risk. Hedging is particularly needed.

1.2 Methodology

This paper will have its focus on currency hedging within the Strategic Asset Allocation and the International Capital Asset Pricing Model. Starting with an introduction of the model, there are several explanations why currency hedging is a crucial point when investors plan to invest internationally. Moreover, weaknesses are considered when an investor wants to invest internationally like the International Capital Asset Pricing Model recommends it. The Model of time varying returns in the ICAPM looks at the Purchasing Power Parity which comes to the result that performance returns are seen very differently in various countries. This implies once more that hedging is needed in every portfolio to protect investors of losses due to negative currency changes.^[4] In chapter three, there is a quantitative approach on how much of the underlying should be hedged and why it makes no sense to hedge a portfolio by 100%. By determing the optimal hedge ratio , a portfolio manager has to keep in mind the time horizon to find the appropriate hedge ratio. A focal point is on Black’s Universal Hedging Model which proves that a 100% hedge is inefficient in every portfolio setting.

Chapter four presents all forms of Asset Allocations according to their time horizons and the investment policy. So, the Tactical Asset Allocation is rather short term related while the Strategic Asset Allocation is more long term focused. Further there is a description of alternative investment for pretty risk averse investors who want to keep their portfolio less risky. The solution here is the so called inflation indexed bond. TIPS offer the investor a very safe investment opportunity because TIPS consider the inflation rate of the country. This means that an investor gets always a positive return because inflation can be fully ignored.

Value- at- risk and the mutual fund theorem as well as upcoming mean reverting show as the last point of the paper how to separate a portfolio between stocks and bonds. It is important if a portfolio is financed by a loan or not. Mean reverting is decisive point which says that some hedging strategies are not needed because unusual returns of an investment are only short term and tend to equalize themselves in the long run.

The paper closes with a conclusion and outlook.

2 International Capital Asset Pricing Model

2.1 The model and assumptions

The CAPM represents a perfect model for a global equilibrium model. This paper has its focus on the international version of CAPM. If markets and conditions were perfect there would be no difference in extending the domestic CAPM to the international one. A large point which makes the ICAPM different and complicated are the different currencies. The reason for changing the implication of the domestic CAPM to the ICAPM is beacause CAPM does not consider currency and changing interest rates.

Further more there are different consumptions preferences in various countries. Developing an ICAPM demands a certain degree of currency hedging. Black’s global equilibrium model, better known as international CAPM, made assumptions which simplify the model. The percentage of currency hedging is very much determined by how risk averse or risk tolerant an investor wants to keep his portfolio. “Black estimated that in equilibrium the fraction of currency that should be hedged is approximately 77 percent.”^[5]

In Blacks model currency means real rates of exchange. Inflation risk is excluded in his model. Risk tolerance is the same for all investors around the world. In this one period model within a two country world, even if the currency is hedged , the investors get different returns because they measure it in different units.^[6]

2.2 Diversifying internationally and the weaknesses of the model

An additional risk when compared to the national market is currency rate risk when investing and diversifying internationally. Quite often international diversification decreases the performance of the portfolio due to the currency risk.^[7] Dumas and Solnik researched if currency risk is included in the world market when investors are going to hedge. They found out that “ the dimension of the exchange risk premia relative to the reward for market risk…”^[8] cannot be compared. Empirical research shows that a model with several risks gives better results than a single factor model. This statement does not agree with the research results of Markowitz ( 1952).^{[9] [10]}

International diversified portfolios are especially risky in bear markets. Research shows that when U.S. markets are decreasing, the cross – border correlation increases significantly. This means that the benefit from international investing is very low when it is particularly needed.^{[11] [12]}

The weakness of the ICAPM is that a world market portfolio has to be found first. The difficulty here is that all markets must be represented according to their capitalization. Even emerging markets should not be ignored. This is a problem which comes up right at the beginning of establishing the world market portfolio. ICAPM shows that investment decisions can be made without looking at a currency because hedging is a tool which provides useful approaches to limit risk for international styled portfolios.^{[13] [14]}

2.3 The model of time varying returns in the International Capital Asset Pricing Model

According to the International CAPM costs are different from the domestic model. In a multiperiod model investors wish to insure themselves against potential risks and changes in future. The forward premium serves as an indicator for future currency prices. In an international adjusted portfolio the Purchasing Power Parity does not hold. This means that investors see returns very differently even if they come from the same asset. The ICAPM with time varying returns has included the currency risk with their covariances.^[15] The model has several investors from different countries who wish to maximize their utility. They have always in mind their need for a future consumption. Every country has its own currency. Investors are free to purchase any asset they want. There is a riskless asset with return and an asset which is not riskless. The excess return varies with the price level of each country. Purchasing Power Parity deviations exist. The currency risk influences the return . All exchange rates from every country are taken together in one index. So hedging becomes easier. In the model there is a budget constraint. The real wealth of the investor is equal to the real gross return multiplied by real wealth in period zero minus real consumptions in period zero. Unplanned consumption goes hand in hand with lower growth of future consumption possibilities. If consumption is to be kept as high as before the unplanned consumption, there has to be an innovation or a new investment strategy. In this model we have only one currency which is just affected by the inflation rate.^[16] “ In addition to the standard international CAPM where investment opportunity stays constant, predictable changes in investment opportunities now induce an effect of intertemporal hedging against future real exchange rate changes”.^[17]

Foreign exchange risk exist while, at the same time, intertemporal hedging demand is present. Incorporating currency risk is one of the most important factors which influences cross-border investment decisions. The dynamic ICAPM shows that hedging is a perfect method for such a portfolio setting.^[18][19]

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^[1] See Johanning/ Rudolph (2000) page 988.

^[2] See van Bergen: www.investpedia.com/printable.asp?a=/articles/04/031704.asp (2004) page 1-2.

^[3] See Markowitz (1952) pages 77-91.

^[4] See Ibbotson et al. ( 1982 ) pages 61-83.

^[5] Litterman (2003) page 56.

^[6] See Litterman ( 2003) pages 56-58.

^[7] See Solnik (1974), pages 48-54.

^[8] De Santis/ Gerard ( 1997) page 1889.

^[9] See De Santis/ Gerard (1997) pages 1888-1889.

^[10] See Adler/ Dumas (1983) pages 925- 936.

^[11] See De Santis/ Gerard (1997) pages 1903- 1906.

^[12] See King/ Enrique (1994) pages 910-919.

^[13] See Jorian/ Khoury (1996) pages 290-295, 316-318.

^[14] See Black ( 1978) pages 1-6.

^[15] See Tat- Chee Ng (2000) pages 6-8.

^[16] See Fama (1991 ) pages 1578-1589.

^[17] Tat- Chee Ng ( 2000) page 14.

^[18] See Tat- Chee Ng ( 2000) page 33.

^[19] See Jorion ( 1991) pages 363- 367.