# How to adjust for risk when determining the price of a security?

When valuing a security future cash flows are discounted to present value. This is for two reasons:

1. You are giving up cash which could have earned certain returns (in government bonds or similar)
2. Future cash flows are not certain

This accounts for the form of the CAPM equation for example. My question focusses on the second element.

My understanding is that it is essentially an expected value of future cash flows and an additional factor (less than one but greater than zero). Let me explain:

Expected value

For the sake of simplicity, take a situation where there is expected to be one cash flow in the future with a corresponding probability such as a lottery. The cash flow is either £1m or £0 and you have a 1/1,000th chance of winning. Thus, the expected value is £1,000. My understanding here is that we've just applied a very high discount factor to the possible future cash flow to account for the risk.

Mathematically speaking, paying £1,000 for this doesn't change your wealth (i.e. NPV=0). But let's say someone offers you £1,000 instead of entering that lottery. A rational investor should accept as you get the same return for lower risk. However, what if they only offered you £1? It would seem silly to accept that. However, there will be a value between those two extremes where one would consider either option appropriate (i.e. you've valued the cash flow). Therefore, there's an additional discount that should be applied.

My question:

1. Is my above reasoning correct and applicable to securities such as stocks (i.e. the above problem but with multiple cash flows)
2. How does one determine the fudge factor to apply? For example, should you accept £800 in the above situation?
3. How would this apply to valuing a company for example. Forecast cash flows presumably are already expected values (otherwise it's a rubbish forecast) so is this additional factor the only discount left to apply to those cash flows?
• The pricing of a security by an individual will depend on their specific risk attitude. So your "fudge" factor will likely differ by individual. The more risk averse someone is the less they will want to invest in securities that may yield very high returns, but with low odds. In other words, the riskier the asset (or the company) the lower the price you are happy to pay. Formally, this can be modelled via utility functions that you apply to the investment problem.
– BrsG
Jul 4 at 10:36