[Music] hello this is David Harper of Bic turtle in this screencast I would like to illustrate or explain a spreadsheet that I uploaded yesterday to the member page of bionic turtle.com for mym candidate customers this spreadsheet illustrates an idea that we see in the Renee stoes readings under operational risk and specifically this is under Enterprise risk management the reading by Brian Noco and Renee stoles and what this spreadsheet illustrates is the idea that a firm can use a credit transition or migration Matrix here at the bottom to solve for the amount of equity Capital that it needs or Equity cushion so in order to explain this I'll start here at the bottom with a an illustrative credit transition or migration Matrix I adapted this from an actual standard and pores credit migration Matrix and what this tells us is that this is a single period Matrix it tells us that if a firm starts here at one of these credit ratings for example a single a that these are the probabilities that the firm will migrate into another rating class during the single period so for example a that starts at single a has a 2% chance of being upgraded two notches from single a to AAA a 3% chance of being upgraded a single Notch to double a and fully an 88% chance of remaining stable in the single a rating so hopefully you can see that with a credit transition or migration Matrix the diagonal has the largest probabilities because over a single period at least the the highest probability is that the firm will remain stable in the rating class so we need this as an input and then what I would just highlight for you because the re the reading can be difficult at first to understand their logic but I would just like to highlight that there's two basic steps here one on the left one on the right the one on the left is the firm decides what its attitude towards risk is it selects a risk orientation and that implies a Target probability of default the lower the firm's risk the lower the probability of default the higher the firm's risk appetite the higher the probability of default that's the first step then given the probability of default The Firm can use the meron model to reverse engineer or infer what its firm value and therefore how much Equity Capital it needs to meet that Target probability of default those are the two steps so let's just take a look at that first so just to illustrate I'll assume that our firm expresses a risk attitude in the following way it would like to fall or be downgraded to speculative or junk status with only 6% probability so that's doubleb because Double B are lower on the S&P scale those are the non-investment grade or speculative or junk scales here's the investment grade so the firm would like to be downgraded to double be or less that's or less with only 6% probability so my spreadsheet tells me that returns an initial credit rating of a what that means is if we look here at the starting at the rating that we start at at the start of the period single a then there is a 2% chance The Firm will be downgraded to a double b a 1% chance to a b a 8% chance to Triple C and a 2% chance to default and so if we add those up that happens to be about 5.8% or or almost 6% and that matches our risk attitude in other words if The Firm starts the period with a credit rating equal to single a then we can see cumulatively there are four outcomes here and about almost a 6% Chance The Firm could be downgraded to doubleb or less speculative status and so this is the Target credit rating that the firm wants it's a single a and if we go all the way over we see it corresponds to Target a probability of default equal to 2% so this risk orientation implies a Target probability of default of 2% now we can go to the Second Step here I'm just carrying over the probability of default and then using the meron model reverse engineering the meron model we need more input assumptions let's say the firm's debt is $10 the expected return on the firm's assets not its Equity is 9% the time period again is a single period one-year model keeping it simple and the volatility of the firm's assets not its Equity is 20% so those are the option like inputs in the meron model and I won't go into the detail in the math here but it tells us that we want a firm or asset value of about $14 against a debt threshold of $10 and that will give us a probability of default of 2% in other words The Firm wants $4 of equity so without going to math on that I do have the diagram here but using the Merton model what we what we said is the firm has $10 in debt and that's the default threshold and we know that the volatility of the firm's assets are 20% and with a growth Assumption of 9% basically we saw for this number here we solved for a when we reverse engineered the bur model we got a result of $14 because if we put in $14 here and grow it at 9% we'll end up at an expected value over the one year of about $15.7 and then with a volatility of 20% on those assets that would get us about 41% above the default threshold which you can see 41% over 20% in standard normal units is just about two standard deviations so by starting with $14 we end up about two standard deviations above the default threshold and that happens to under a normal assumption imply about 2% of the area under the total curve is in this tail in other words that implies a 2% % chance that the firm could end up here below the default threshold and in default so you see how we really started with we want we want a number here that gives us 2% of the area under here that number here happens to be a firm value of $14 so that number we started with targeting a probability of 2% and it and reverse engineering we come back and find out that what we need for a firm value is therefore $14 we need $4 of equity cushion $4 of equity cushion will give us a 2% probability of default which again will meet our Target risk orientation working backwards the other way finally the $4 in equity implies a firm value of $14 because that means that we'll be two standard deviations above the default Threshold at the end of the period with therefore a 2% probability of default with a 2% probability of default we need to start with an initial credit rating of a single a because that's the rating that if we start with we have only a 6% chance of being downgraded to speculative status so I hope that is a helpful walkth through of that spreadsheet and you can see it invokes uh at least several Concepts that we review primarily in the re Renee stalles readings under operational risk this is David Harper the bino turtle L spere [Music] time