39.308 Seiten

Assessing the Impact of XML/EDI with Real Option Valuation

von Dr. Shermin Voshmgir

vorherige Seite | zur Übersichtsseite | folgende Seite

Statistik und Sichtungsnachweis dieser Seite findet sich am Artikelende

 Zuletzt bearbeitet: 2020-01-24 14:10:01 [[Benutzer:|]] BauernOpfer, Fragment, Gesichtet, Luehrman 1998, SMWFragment, Schutzlevel sysop, Svr

Untersuchte Arbeit:
Seite: 78, Zeilen: 2-29
Quelle: Luehrman 1998
Seite(n): online, Zeilen: 0
[Step 1: Calculating Cumulative Volatility]

When deferring an investment decision, the asset value may change and affect the investment decision for the better while waiting. That possibility is very important, but naturally it is difficult to quantify because of the uncertainty as to how the future asset values will change. The most common probability-weighted measure of dispersion is variance σ2. Variance is a summary measure of the likelihood of a random value far away from the average value. The higher the variance, the more likely it is that the values of an investment project will be either much higher or much lower than average.

How much things can change while one waits, also depends on how long one can afford to wait. For business projects, things can change a lot more waiting two years than if waiting only two months. Thus the measure of the total amount of uncertainty is variance per period σ2 times the number of periods t. This is referred to as cumulative variance.

Cumulative Variance = Variance per period x number of periods = σ2 t

For mathematical convenience, instead of using the variance of project values, Luehrman (1998) suggests to use the variance of project returns, in other words to work with the percentage gained or lost per year. There is no loss of content because a project's return is completely determined by the project's value:

Return = (Future Value minus Present Value) over Present Value

The reason for doing this is that the probability distribution of possible values is usually quite asymmetric; value can increase greatly but cannot drop below zero. Returns, in contrast, can be positive or negative, sometimes symmetrically positive or negative, which makes their probability distribution easier to work with.

Second, it helps to express uncertainty in terms of standard deviation σ, rather than variance σ2. Standard deviation, which is simply the square root of variance, expresses just as much about uncertainty as variance does, but it has the advantage of being denominated in the same units as the investment project being measured.

Luehrman, T.A. 1998, “Investment opportunities as real options: Getting started on the numbers”, Harvard Business Review, vol. 76, no. 4, pp. 51 - 55

Quantifying Extra Value: Cumulative Volatility.

Now let’s move on to the second source of additional value, namely that while we’re waiting, asset value may change and affect our investment decision for the better. That possibility is very important, but naturally it is more difficult to quantify because we are not actually sure that asset values will change or, if they do, what the future values will be.

[...]

The most common probability-weighted measure of dispersion is variance, often denoted as sigma squared2 ). Variance is a summary measure of the likelihood of drawing a value far away from the average value in the urn. The higher the variance, the more likely it is that the values drawn will be either much higher or much lower than average. [...]

We have to worry about a time dimension as well: how much things can change while we wait depends on how long we can afford to wait. For business projects, things can change a lot more if we wait two years than if we wait only two months. So in option valuation, we speak in terms of variance per period. Then our measure of the total amount of uncertainty is variance per period times the number of periods, or σ 2 t.

This sometimes is called cumulative variance. An option expiring in two years has twice the cumulative variance as an otherwise identical option expiring in one year, given the same variance per period. Alternatively, it may help to think of cumulative variance as the amount of variance in the urn times the number of draws you are allowed, which again is σ 2 t. [...]

First, instead of using the variance of project values, we’ll use the variance of project returns. In other words, rather than working with the actual dollar value of the project, we’ll work with the percentage gained (or lost) per year. There is no loss of content because a project’s return is completely determined by the project’s value: The probability distribution of possible values is usually quite asymmetric; value can increase greatly but cannot drop below zero. Returns, in contrast, can be positive or negative, sometimes symmetrically positive or negative, which makes their probability distribution easier to work with.

Second, it helps to express uncertainty in terms of standard deviation rather than variance. Standard deviation is simply the square root of variance and is denoted by o . It tells us just as much about uncertainty as variance does, but it has the advantage of being denominated in the same units as the thing being measured.

 Anmerkungen The source is given, but it is not made clear that the text is so extensively copied - no quotation marks. Sichter (SleepyHollow02) Schumann

vorherige Seite | zur Übersichtsseite | folgende Seite
Letzte Bearbeitung dieser Seite: durch Benutzer:Schumann, Zeitstempel: 20200124141109
Nutzung von Community-Inhalten gemäß CC-BY-SA, sofern nicht anders angegeben.
… weitere Daten zur Seite „Svr/078
SleepyHollow02 +
(SleepyHollow02) Schumann +