# Security equivalent

The security equivalent of an uncertain outcome of known probability, a lottery, is that amount of money at which a person is indifferent between the amount of money and the lottery.

Anyone who buys a company to invest money acquires uncertain returns in the future. To simplify matters, a current amount of money is exchanged for an uncertain payment at a single future point in time.

the Company valuation verlangt in diesem einfachen Gedankenexperiment die Beantwortung dreier Fragen.

1 question: What is the probability distribution of the amount z returned to the investor at the future point in time? What is the distribution type, what are the parameters, in particular the expected value EN and the scatter or the variance Var [z]? The answer depends on the specific company and is given by the financial analysis.

2nd question: If, at the future point in time when the uncertain payment of known probability distribution will occur, many people compare it to a certain amount of money s at the same point in time, what would be the amount of money that many people would be indifferent to? This amount of money is the security equivalent. In a financial market, s is of course not determined on the basis of the preference of an investor, but on the basis of the risk preferences of numerous market participants and is therefore a market variable.

3rd question: What is today's value, the present value of the security equivalent? Here, the interest rate, which describes investments and borrowings under security, is discounted. As before, this interest rate is also denoted by i (like interest).

Overall, the current value of the future uncertain payment z is given by s / (1 + i), assuming that the uncertain payment will be made in one year.

If the above-mentioned assumptions of the hybrid model are given and for this reason s = EN - (a / 2) * Var [z], then the “Unter
business value expressed by (EN - (a / 2) * VarH / (1 + i).

Bei einer anderen Umrechnung der unsicheren zukünftigen Zahlung wird das Sicherheitsäquivalent umgangen und es wird versucht, das Risiko der unsicheren Zahlung z dadurch zu berücksichtigen, daß mit einem über dem Zins liegenden Cost of capital diskontiert wird. Dieser Satz sei mit r bezeichnet, und der „Unternehmenswert“ ist dann gleich EN / (1 + r) . Hier werden die in den oben gestellten Fragen 2 und 3 beschriebenen Schritte in einen einzigen zusammengefaßt.

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