| Risk Management is older than written history. | | | | historical data used to construct the VaR estimate |
| However, it wasn't until the mathematical advances in | | | | contains useful information to forecast the loss |
| the 18th and 19th centuries when actuarial science | | | | distribution. Value at Risk aggregates all of the risks in |
| and civil engineering where flourishing did proactive | | | | a portfolio into a single number ideal for reporting to |
| risk management evolve. Financial risk came later as | | | | management or in shareholder reports. |
| an invention of the second half of the 20th century. | | | | One of the tools for assessing VaR is Monte Carlo |
| Before, gold acted as a hedge against interest rate | | | | simulation. Like most financial models some |
| or foreign exchange risk but short-term interest rate | | | | assumptions are made first such as the distribution of |
| changes or extreme currency fluctuations made | | | | changes in asset prices are normally distributed. Data |
| financial risk management difficult. In the early 197os | | | | is then collected to estimate the parameters of the |
| when the gold standard was dropped and stagflation | | | | distribution (ie standard deviation). Monte Carlo then |
| was the word of the day financial risk management | | | | provides several sets of possible future outcomes |
| had become more important than ever. But how? | | | | given the changes in asset prices. The portfolio is |
| Fortunately, Modern portfolio theory was introduced | | | | then revalued with each outcome leaving you a set |
| by Harry Markowitz back in 1952 with his paper | | | | of portfolio valuations relating to the set of possible |
| "Portfolio Selection," and a new breed of quantitative | | | | outcomes of the asset price change. Then from this |
| mathematicians were finding their way to Wall Street. | | | | distribution of data you take say a 95 or 99 |
| With the rise of "quants" and the fall of markets on | | | | percentile (the 1% part of 1% 1 day VaR) loss as |
| Black Monday October 19, 1987 had finally pushed | | | | VaR. |
| risk management to the front of every boardroom | | | | One of the common questions with Monte Carlo is |
| agenda. Value at Risk was born from the cross | | | | how many simulated asset price changes should be |
| breeding of sound knowledge of operational risk and | | | | used. It really depends on the complexity of the |
| a blend of modern portfolio principles. | | | | portfolio. For non-linear instruments like options more |
| A recent risk management study by | | | | simulations would be prudent than linear asset |
| Pricewaterhousecoopers found that the 3 most | | | | portfolios. There are ways to improve accuracy in |
| important objectives of risk management were | | | | Monte Carlo models such as antithetic variance |
| identifying new and emerging risks, measuring and | | | | reduction allowing for less simulations for a given |
| monitoring risk and being able to communicate these | | | | portfolio. |
| risks to the executive team. Value at Risk fulfills the | | | | Here is a simple example of the VaR concept with |
| last 2 criteria quite well. | | | | our Monte Carlo data in hand. Assume that our |
| VaR as it's also known is a market risk measure for | | | | distribution of possible one day changes yields a 2% |
| extreme or highly unlikely outcomes. Denominated in | | | | probability that a portfolio loss will exceed $10,000, a |
| units of currency it is a statistical measure of the | | | | 1% probability the loss will be between $8,000 and |
| potential loss that a portfolio would be subject too | | | | $10,000 and a 2% probable loss of between $6,000 |
| generally with a 1 day time horizon (you may have | | | | and $8,000. There is then a 5% probability that the |
| heard of 1% 1 day VaR). It can be expected to | | | | loss will exceed $6,000. If we use this 5% probability |
| close out or hedge a portfolio within 1 day. Indeed | | | | (5% 1 day VaR) as the criteria to define a loss due |
| there are instances when liquidating a portfolio may | | | | to normal market conditions then $6,000 is the Value |
| take several days such as with credit products. In | | | | at Risk. |
| this case, one can use an average time horizon for a | | | | Given the ability for risk managers to easily report a |
| multi- horizon portfolio. | | | | single number to the board or to her regulators it's |
| Of course there are assumptions with VaR as well | | | | no wonder that VaR has remained an important |
| such as the portfolio remaining constant over the | | | | measure of risk. |
| time horizon. A VaR model also assumes that the | | | | |