Estimating Value at Risk (VaR)

For example, think about how portfolio construction can impact the VaR calculation. If you held cash on 19 October 1987, you'd have probably done better than somebody who was fully invested. What does that tell you about VaR?

Bingo!

No, actually. The individual portfolio will help determine VaR.

When you think of VaR, you'll need to first take into consideration the holdings of the portfolio. That's because there could be minimal risk from holding cash or lots of risk from multiple risk exposures through a convertible foreign bond. The process for breaking down a portfolio's risk is called risk decomposition, and it can vary significantly between different securities, so it's crucial to get it right.

Then the second step in the VaR process is gathering historical data for each risk factor. Why might that be helpful?

No, actually. Remember you're working with individual risk factors, so you'd want more specific data than the portfolio value.

That's not it. Dividends aren't the best approach for determining risk factors, so that historical value isn't much help.

Way to go! Historical data will help calculate the specific standard deviation for each individual risk factor, so you'd have a detailed view of how the portfolio might change in the future. The historical data collection is referred to as the lookback period, and it's where you would collect the average return for each holding, along with each holding's standard deviation.

During the lookback period, it's crucial to break down each individual holding because sometimes risks can be masked at the portfolio level, like when you write an option with unlimited risk. Even though it might have paid off in the past, there's some significant risk that can impact the future. What's a good approach to address this issue?

Exactly!

That's not it. That wouldn't give you an accurate risk assessment because it's based on your personal opinion, which should naturally reflect what's in your portfolio. You wouldn't structure your holdings to lose money.

You would need to modify the data to represent an accurate historical picture of the portfolio. That way the risk is captured. To ensure that historical data reflects the relationship between the portfolio and individual holdings, you also need to adjust for correlation. This means that the historical data should capture the degree to which different assets within the portfolio move together (or independently). The adjustment process involves aligning the correlation of the historical data with the correlation among the portfolio components. Once this adjustment is made, a VaR (Value at Risk) estimation technique can be applied to quantify the potential loss in the portfolio over a specific time frame, given normal market conditions and a certain confidence level.

To summarize: [[summary]]

During the market crash on 19 October 1987, the stock market dropped over 22%. That's a huge plunge on one day! So understanding the risk of a portfolio is crucial, especially when events like the October crash can occur.

VaR should be based on market risk

Holdings in the portfolio can impact VaR

It helps to value the portfolio at various points in time

It helps to determine how dividends impact the cash balance

It helps calculate the standard deviation of the risk factor over a time period

Modify the historical data to align more closely with a typical historical experience

Modify the data to reflect your personal opinion on the future of the stock market and your portfolio

Continue

Continue

Continue

Continue