Cointegrating Vectors in Panels and Reversal Time

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Portfolio Theory Development

Markowitz (1952) on his theory on portfolio selection states that to execute the choice of a portfolio process investor will maximize the discounted value of future returns (E) and mini-mize variance (V). This combination of securities, which reflect a diversification in the portfo-lio, resulted in maximum expected return with minimum variance (E-V rule) then defines as an efficient portfolio.
Markowitz argues that the model should use covariance instead of variance to reflect the overall securities in the portfolio. Applying this method to debt portfolio, means that return for the investor and or creditors is the cost for debtors. Since investors/creditors will choose the effi-cient frontier of portfolio available in the market therefore debtors has to trade off the cost of borrowing (return for investors/creditors) and risk of issuing debt (covariance of the overall securities).
Tobin (1958) develops Markowitz theory by introducing riskless asset to a portfolio. He argues that investors prefer to hold cash investment with yield of zero (assumed to be riskless invest-ment), for liquidity reason and risk-avoiding behavior, and investing in yielding investments. Investors can analyze the future probability of the portfolio by deriving indifference curves from combinations of expected returns and risks (standard deviation) on non-yielding and yield-ing investments with different interest rates. So first, investor has to choose yielding invest-ments and then second, combining that basket of investments with a riskless investment.
Yielding investments (or risky investments) can be a composite of investments e.g. bonds and other debt instruments differing in maturities, debtors, and other features. Hence, investors will maximize the utility function of the future probabilities. The optimum portfolio is then defined as the highest possible expectation of return available to investors at level of risks; then it is called as dominant pairs of investment combinations. A balance of combination between riskless investment and risky investments constructs the dominant pairs.
A risk-free rate investment in a portfolio theory can diversify away the risk on the portfolio arising from risky investments. The efficient portfolio provided by the efficient frontier line then nowadays called as the capital market line. In the term of debt portfolio, the debtors then pursue issuing riskless securities e.g. treasury bills so that the market can generate the market efficient frontier available to the investors. The debtors’ task is then to manage the trade-off between cost of borrowing (return for the investors) and risk (standard deviation or covariance).
Sharpe (1964) points out that the two theories above do not reveal the market equilibrium under uncertainty. He argues the effect of an investment on an investor’s over-all investment opportunity risk depends not only to the expected return and risk, but also to its correlation with other available investments. The condition where correlation is considered in determining probabilities of expected returns and risks must be hold in equilibrium.
Sharpe model is an improvement of Markowitz and Tobin theories. He states that assets (investments) price will cause investors’ actions with “new combination or combination become attractive”. This process further will change the asset prices until all assets lying in capital market line. This is the equilibrium condition where there is simple linear relationship between expected return and standard deviation for efficient combination in the risky assets. This relationship is consistent or then called as systematic risk. On the other hand, there is a part of an asset’s risk that is due to its correlation with the return on combination cannot be diversified away when asset is added to the combination. Two combinations of assets will be tangent in an equilibrium.
The expected rate of return of investing in riskless asset and some risky assets is derived as:
ERc  aERp  (1 a)ERa (1)
ERc corresponds to expected rate of return on investing in riskless and risky assets, ERp is riskless interest rate, Era is expected rate of return on risky assets, a is proportion of fund invested in riskless asset, and 1-a is remainder proportion of fund invested in risky asset. The standard deviation of a combination of investments is: σRc = [a2σ2 Rp+(1-a)2σRa 2+2rpaa(1-a)σRpσRa]½ (2)
These three developments of portfolio model above have been used nowadays in assessing and managing risk. The concept is used for both asset position and liability position by using value at risk. Value here can be value of assets/investment or value of debt which are estimated to be at risk.
Sharpe also mentions that by holding the position on assets and liabilities the concept of Capital Asset Pricing Model (CAPM) can be applied. Assets and liabilities can be denominated in domestic and foreign currency; and for the latter the exposure of risk is higher coming from fluctuation of foreign exchange rate. This is also a concern for debt agency in managing the risks.
To summarize, the theory on portfolio shows a development in the portfolio theory where Markowitz introduces a portfolio consisting of combination of different investments by trading-off the overall returns and risks. Tobin introduces risk-free rate investment to the portfolio constructed by Markowitz, and then Sharpe completes the model by introducing correlation in determining the optimal portfolio from Tobin model.

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1 INTRODUCTION .
1.1 Background
1.2 Problem
1.3 Purpose .
2 BACKGROUND
2.1 Literature
2.2 Previous Studies .
3 THEORY
3.1 Portfolio Theory Development
3.2 Hypothesis
3.3 Causes of Inefficiency in Foreign Debt Portfolio
4 METHOD
4.1 Unit Root Testing .
4.2 Cointegration Testing
4.3 Cointegrating Vectors in Panels and Reversal Time
5 DATA AND RESULTS.
5.1 Data and Preliminary Findings
5.2 Panel Unit Root Testing
5.3 Cointegration Testing
5.4 Cointegrating Vectors in Panels and Reversal Time
6 ANALYSIS
6.1 Preliminary Findings Analysis
6.2 Econometrics Model Analysis
6.3 Economic Analysis
7 CONCLUSIONS