How much risk are you willing to take? Quantifying your risk with VaR | by Dongho Kim | November 2023

“Hey my man how bad do you want it?
Do you know how many cats I’ve thrown and they never caught it?
I told them to bring their text but they never did
Are you afraid that someone will cheat you, cheat you, delete you, reject you and cut you short?
– From “How Bad Do You Want It” by KRS-One

KRS-One definitely favors risk takers. Perhaps this is how he earned his reputation as one of the greatest lyricists of all time. As you know, high risk goes hand in hand with high return. But most of us are not built that way. According to survey conducted by Northwestern Mutual in 2019less than half of Americans were comfortable with taking financial risks for higher returns. In other words, we are mostly risk averse.

But by how much? Most of us don’t really keep track of how much loss we can tolerate. At the same time, we also do not fully know how big our potential loss can be. In this story I will try to suggest an answer to this using a Value-at-Risk (VaR) model so that you can actually estimate the potential loss of your portfolio and factor it into your risk profile.

Value-at-risk (VaR) is a measure of risk that represents the maximum potential change in the value of a portfolio of financial instruments with a certain probability over a certain period of time. In simpler terms, it answers the following questions: How much value can the portfolio lose in the selected time window? How much money is at stake?

To find out, we need some information:
1) simulation period,
2) average historical daily returns,
3) the portfolio’s historical daily volatility,
4) observation period,
5) confidence level and of course
6) the number of simulations we run.

Volatility

Let’s start with volatility. We will apply Exponentially Weighted Moving Average (EWMA) method because it reflects the historical trend by placing more weight on recent observations than past ones. Let’s look at the formula and break down the components.

st = Estimated volatility at time t
rt-1 = Daily return at time t-1
λ = decay factor
σt-1 = Volatility at time t-1

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