Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Value at Risk

Value at risk represents the amount of money at risk with a probability of p over a time period t.

The cutoff percentile approaches 1/2 as volatility increases. As the daily value at risk, or mean annual return, increases, the cutoff percentile decreases.

Formula

Erfc[(5*Sqrt[5]*(Log[Quantity[1, "USDollars"^(-1)]*QuantityVariable[Subscript["V", "i"], "Money"]] - Log[Quantity[-1, "USDollars"^(-1)]*QuantityVariable["VaR", "Money"] + Quantity[1, "USDollars"^(-1)]*QuantityVariable[Subscript["V", "i"], "Money"]] + QuantityVariable[Subscript["r", "m"], "Unitless"]/250))/QuantityVariable["σ", "Unitless"]]/2 == QuantityVariable["p", "Unitless"]

symbol description physical quantity
σ volatility "Unitless"
Vi initial value "Money"
VaR daily value at risk "Money"
rm mean annual return "Unitless"
p cutoff percentile "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Value at Risk"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Value at Risk"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Value at Risk"], {QuantityVariable["p","Unitless"] -> Quantity[1.`, "Percent"], QuantityVariable[ \!\(\*SubscriptBox[\("V"\), \("i"\)]\),"Money"] -> Quantity[100, "USDollars"], QuantityVariable["VaR","Money"] -> Quantity[50, "USDollars"]}]
Out[3]=

Publisher Information