Calculating VaR in the Case of the SPDR S&P 500 ETF Trust (SPY)

In this article, let's take a look at the Value at Risk (VaR), which is a probabilistic method of measuring the potential loss in a portfolio value over a given time period and for a given distribution of historical returns. VaR is the dollar or percentage loss in portfolio value that will be equaled or exceeded only X percent of the time.

There is an X probability that the loss in portfolio value will be equal to or greater than the VaR measure. The analyst must select the X percent probability and the period over which VaR will be measured.

It is common to use a one-day period.

There are various methods to calculate but let's concentrate on the Monte Carlo Simulation. This method generates a huge amount of possible outcomes from the distributions of inputs specified by the analyst.

We are going to calculate it in the case of THE SPDR S&P 500 ETF Trust (SPY).

The ETF seeks to track the price performance of the underlying holdings in the S&P 500 Index. The S&P 500 Index measures the performance of the large-capitalization sector of the U.S. equity market. The Index is a capitalization-weighted index of a broad range of industries chosen the market size, liquidity, and industry group representation. It is a popular proxy for the U.S. market and is an indicator of the economic health. It is perfect for investors looking for diversification across sectors at a low cost. The top holding list includes companies such as Apple Inc (AAPL), Exxon Mobil Corp (XOM), Microsoft Corp (MSFT) and Johnson & Johnson (JNJ).

Suppose you are a risk manager and calculate the daily 1% VaR. The VaR (1%) indicates that there is a 1% chance that on any given day, the portfolio will experience a loss of $1,831,934,592 or more. In other words, there is a 99% chance that on any given day the portfolio will experience either a loss less than $$1,831,934,592 or a gain.

The loss represents 1.2% of the portfolio value. In one day, there is a 1% chance that the portfolio has a loss of 1.2% or greater. But there is a 99% chance that the loss could be less than 1.2% or a percentage gain greater than zero.

Final Comment

The Monte Carlo simulation approach calculates a portfolio for a large number of risk factor values, randomly selected from a normal distribution.

For investors seeking to invest in large cap U.S. equities, the SPY is an alternative due to its diversification and attractive total return that ranks high when compared to its peers over the last three years. Investors who are looking to complement this fund with smaller-cap stocks should look at Vanguard Extended Market Index ETF (VXF).

Published on Aug 29, 2015
By Omar Venerio
Capital Markets, Derivatives and Financial Management Professor, Master in Finance and CFA candidate. I am an independent trader of stocks and options and passionate about the stock market.

Copyrighted 2016. Content published with author's permission.

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