Market Risk Implied or Inherent

To extend on from our previous article on inherent risk [ LINK ] we will dive a little bit deeper into the importance of inherent risk using an example from the domain of market risk measurement.
  

In market risk there are many ways to calculate the cost of exposure from risk but two fundamental techniques come to mind, these are alternate schools of thought might I add and I will explain both techniques in brief below to evidence the importance of measuring inherent risk.

The Implied Forward Rate

The first valuation technique is away from inherent risk.

One technique to calculate risk is to look at the implied forward price for an asset, say the price of gold in the next 30 days. The implied forward price is the cost from volatility of an underlying instrument (gold in this case) when parameters are fed into a model such as an option price model [ LINK ], the result of this calculation is the implied forward rate.

The Spot Rate

The second technique, the Spot Rate is pretty much observable inherent risk.

Another technique that could be used to understand the cost of risk from volatile gold prices would be to review the raw historical univariate time series alone. The pure data signal of prices or the inherent price, the spot rate as traders refer to it.

These two calculations will both give you a price for risk but more often than not, both these calculations will result in different prices. This deviation in prices between the inherent spot rate and the implied forward rate is so common that market risk managers measure the difference between these two values of risk, something they term as the delta: Delta measures the rate of change of an option value with respect to changes in the underlying inherent asset's price.

  

Different methods to value uncertainty

Why are we doing all of this, why not just take the price of risk from the underlying spot rate, the inherent risk and just as it is?

The real cost of risk is not volatility or randomness alone but your objective against this background of inherent uncertainty, it is also your error in being able to read the forward market. When we control something, when we have an objective in the background of randomness we can alter both randomness itself and be impacted by the feedback loop of it. Finally, we also suffer perception error from simply being in the game of randomness!

Why is there a price spread between observed inherent uncertainty and the calculated implied forward rate, surely these two numbers should be the same?

Firstly, no model of uncertainty is perfect but the difference between these two places (inherent and implied) will give you insight into whether your objective was profitable or not, whether an arbitrage opportunity exists or not, whether the assumptions under your objective have error or the prime directive itself is misaligned and so on.

In risk measurement we are often trying to resolve gaps in our knowledge of what is going on around us and of course accept that the human perception of randomness might have some kind of affect / effect on our objectives.

If risk is the effect of uncertainty on an objective(s), all uncertainty (variance, volatility, randomness, measurement error, opaque causality ...) can be summed up to being epistemic; our inability to read the future and respond to it in a timely and appropriate manner.

Knowing just the Implied Forward Rate, your world with control is equivalent in some respects to viewing uncertainty with only one eye. Viewing risk with implied forward rates, stochastic spot rates, spreads between these two places, changes in spreads through time will allow us to understand risk (effect(s) of uncertainty) from many different perspectives and that reduces our epistemic gaps of uncertainty.