Friday, December 20, 2013

Quantifying Risk

12:06 PM


Lightning and lotteries

According to the National Oceanic and Atmospheric Administration, the odds of becoming a lightning victim in the United States in any one year is 1 in 700,000. Your odds of winning the jackpot at Lotto 6/49 is 1 in 13,983,816. So you are 20 times more likely to be struck by lightning than winning the jackpot. If you paid $3 for your ticket and the jackpot is $5 Million, your expected gain is $0.36 and your net expected loss for your $3 investment is $2.64.

We tend to think that we will almost certainly will never be struck by lightning, while today may just be our lucky day for Lotto 6/49.

Getting struck by lightning is a risk with known odds and outcome. If you walk in an open field during a thunderstorm with an umbrella pointing upwards, your odds become considerably higher. Knowing the danger, most of us avoid this risk by staying out of harm's way.

There is also a risk of loss with the lottery ticket purchase. The loss is quite small ($3.00), and it may be viewed as a harmless entertainment expense. But the point is that you are trading a small loss for a very unlikely gain that can have a large impact on your life.

By definition, a risk carries uncertainty. In exchange for a potential payoff, we take a chance of incurring a loss. Each risk has its own odds and the impact can be small or large if it occurs.

Why think about risk?

When it comes to retirement planning, we must consider that our livelihood will come from invested assets, public and private pensions. We are no longer counting on indefinite and renewable employment income.

Examining each of the potential risks can help us make decisions on how we can minimize the odds of running out of money under all potential situations that may unfold in the future.

As with lightning and lottery, when assessing risk, we must determine its likelihood and the magnitude of the outcome. Armed with this information we can then decide whether we want to apply techniques to reduce, eliminate, transfer, or retain the risk.

Assessing risk

The likelihood of a risk is the odds it will happen, and its magnitude is the amount or severity of the loss.

There are several approaches to quantifying risk. Numerous different risk formulae exist, but perhaps the most widely accepted formula for risk quantification is:
Risk = Rate of occurrence X Impact of the event
Three approaches can be used to assess post-retirement risks:

  1. Determining the odds for the occurrence,
  2. Evaluating the impact of a risk to a moderate change in outcome using sensitivity testing, or
  3. Gauging the impact of an occurrence with stress testing.

The risk analysis in RetireWare uses a combination of these approaches, with an emphasis on stress testing.

The importance of the longevity risk
"Longevity: The Underlying Driver of Retirement Risk"
 – Society of Actuaries report
The financial aspect of a successful retirement depends on the level of spending, available capital and sources of guaranteed income to finance expenses over the retirement period. Spending, initial capital and guaranteed income are predictable.

Investment returns can be managed to a degree with diversification, conservatism and hedging, but still carry significant uncertainty and can wreck wealth if poor returns prevail at the onset of retirement. Longevity for an individual is completely unpredictable, but life expectancy is rising and this is expected to continue with improvements in lifestyle and medical care.

Appropriate levels of spending ultimately depend on the duration over which they apply. This makes longevity in our view the most important factor to which other risk factors are subordinate.

Looking at the possibilities
“All models are wrong, but some are useful.”
– George Box, Professor Emeritus of Statistics
A risk cannot be evaluated in a  vacuum in the real world. It interacts with other factors and other risks. In other words, more than one adverse risk event can take place at the same time.

We developed a mathematical model to assess and quantify exposure to post-retirement risks. An objective function quantifies the success of the retirement plan with respect to each risk under consideration by looking at demographic and economic scenarios where a particular risk occurs and measuring the impact on the retirement budget.

The quantification of risk follows a stress testing approach that considers the odds of each economic and demographic scenario, and the set reproduces all possibilities to closely match the expected outcome and volatility used for the model.

Risks under consideration are: longevity, market, inflation, sequence of returns, long-term care and loss of spouse. For each risk, the risk success value depends on the degree to which expenses are covered where the risk occurs in  a subset of the economic and demographic scenarios.

Scenarios combine different end points of life expectancy and economic environment for equities, bonds, interest rates and inflation. Each scenario applies to one or more risks. The success measure is based on the present value of the shortfall of assets required to meet retirement income goals.

The degree of success values for each risk is an average of the results obtained for the applicable scenario subset. Results are rated on a scale from 0% to 100%, with 100% being the perfect rating, where the risk is completely managed.

Based on the individual’s retirement financial needs and aspirations, each risk's index value evaluates how the risk is managed. Taken together, the risk measures provide an overall evaluation of the current post-retirement risk strategies in place and highlights areas of weakness that need to be addressed.

Two other measures complement the risk analysis results: the expected estate compared to the estate objective goals and the degree to which sources of lifetime income covers essential and discretionary expenses.

The income coverage measurement provides information on "income coverage" and "essential expenses coverage". If there is a detailed budget, the results include the average percentage that sources of lifetime income (annuities, Government and private pensions) are able to cover the retirement income goal. For example, if the goal is $50,000 per year and lifetime income sources are at $20,000 on average, the income coverage is 40%. 

Risk management plan

Once risks have been assessed, strategies can be adopted to improve areas of weakness in the retirement plan. These strategies fall into one or more of these four major categories:

  • Avoidance (eliminate)
  • Reduction (mitigate or control)
  • Transfer (outsource or insure)
  • Retention (accept and budget)

Risk analysis results and management plans should be updated periodically to evaluate whether risk levels have changed or whether the strategies in place are still effective.

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