Tobin separation

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The Tobin separation (also Tobin separation theorem ) is a term from capital market theory . With the Tobin separation, a portfolio is divided into a risk-free and a risky component. Accordingly, it separates the risk-linked and the risk-free interest rate . Briefly, the composition of the is market portfolios of the risk attitude of investors independently.

The concept goes back to the American economist James Tobin .

The separation concept in general describes the independence of optimal decisions from certain characteristics of the decision or situation. The Tobin separation describes the independence of the decision on the optimal composition of a securities portfolio from the risk attitude . The related concept of Fisher Separation describes the optimal investment decision independent of financing.

Explanation

Budget and preferences in the - diagram

The portfolio theory is the so-called - in principle. It analyzes situations against the background of returns (expected value) and risk (standard deviation). Another important assumption is risk averse investors.

The Tobin separation is an assumption of the CAPM that assumes that in the capital market equilibrium the risky part of the portfolios of all investors is structured identically, regardless of their risk preference. This part is also known as the market portfolio . This also means that the optimal mix of risky investments remains unchanged, regardless of how much an investor spends on initial equipment for consumption purposes.

In other words: portfolio management deals with two basic questions that can be solved separately:

  1. Determination of a market portfolio : is identical for all investors, information about the investors (such as their risk attitude ) is not required (the interest rate and distribution parameters of the risky investments must be known)
  2. Determination of the individual risk aversion : the percentage of assets in the market portfolio that an individual investor would like to hold must be determined.

The Tobin separation describes the decoupling of the structure and the volume of riskily invested assets. As part of the CAPM and assuming the market clearance , the Tobin separation leads to the tangential portfolio being identical to the market portfolio.

For the illustration on the right, this means: two investors A and B have different preferences (red and green curve), which only means that they will ask different amounts of the market portfolio M. The budget line is identical for both investors. All possible combinations are on the capital market line .

In addition, it is a central insight of Merton's solution to the modern consumption-investment problem that the assumption for the intertemporal consumption problem can be adopted so that the deficits of the CAPM (no intertemporal consideration, quadratic utility function) can be overcome.

Evidence of the Tobin separation

The Tobin separation can be shown on the basis of portfolios with risk-free investment and debt options.

Risk-free investment opportunity

If there is a risk-free form of investment (assumption of the classic CAPM), mixtures of any portfolio (with the exception of the market or tangential portfolio) and the risk-free investment are inefficient.

Only mixtures of a tangential portfolio and a risk-free investment are efficient. The totality of the possible mixes forms the capital market line. The efficiency of the portfolios on the capital market line is given by the favorable risk-return ratio from the perspective of risk-averse market participants (assumption of the CAPM). Each unit of risk assumed is rewarded at the most by the market, which reflects the increase in the capital market line (market price of the risk).

Risk-free debt option

With a risk-free debt option, mixtures of debt and tangential portfolio are efficient. In doing so, the debt option must only be used when there is a certain return. Otherwise the normal efficiency line applies.

Investment and debt

A distinction can be made between the debit interest rate and the credit interest rate.

  • If the debit and credit interest rates are identical, the efficiency line is a straight line running from the risk-free interest rate through the tangential portfolio.
  • However, if the credit interest rate is lower than the debit interest rate, the tangential portfolios are not identical. In this way, the efficiency line includes a part of the efficiency line without the possibility of debt or investment.
  • In the banking case, the credit interest rate is higher than the debit interest rate:
    • Efficient portfolios would not exist if there was unlimited debt.
    • Debt can be limited, e.g. B. by the Banking Act . For the sake of simplicity, it is assumed that the leverage ratio is less than or equal to one.

criticism

One of the problems with the Tobin separation is that the risks implied in the interest rate relate to the entire market and not to all components of the individual risk assessment. There may also be other risks, such as reinvestment risks in the event of changes in interest rates and the associated changes in income, which are difficult to capture with the model.

Individual evidence

  1. ↑ Anderegg, Ralph. Fundamentals of monetary theory and monetary policy. Walter de Gruyter GmbH & Co KG, 2007. p. 116.
  2. ↑ Adam-Müller, Axel FA. International corporate activity, exchange rate risk and hedging with financial instruments. Springer-Verlag, 2013. p. 7.
  3. ^ Schneider, Dieter. Investment, Financing and Taxation, 7th edition, Gabler, 1992. p. 423.
  4. ^ Spremann, Klaus. Finance. Walter de Gruyter, 2010. p. 230.
  5. ↑ Braun, Thomas. Investment and financing: conceptual foundations for decision-oriented training. Springer-Verlag, 2009. p. 147.
  6. ↑ Zhu, Mei. Insurance securitization with catastrophe bonds: with special consideration of their influence on the economic target capital. Vol. 12. Verlag Versicherungswirtsch., 2009. P. 109.
  7. ↑ Anderegg, Ralph. Fundamentals of monetary theory and monetary policy. Walter de Gruyter GmbH & Co KG, 2007. p. 117.

literature

  • Tobin, James. "Liquidity preference as behavior towards risk." The review of economic studies (1958): 65-86.
  • Adam-Müller, Axel FA. International corporate activity, exchange rate risk and hedging with financial instruments. Springer-Verlag, 2013. Chapter 1.2 Separation , p. 7ff.

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