What Is Default Probability?
Commonly referred to as Default Probability, it is the financial term used to describe the likelihood of a default in a particular time frame; it quantifies the chance of a borrower defaulting on their loan.
Whether it is a country looking to borrow resources to support expenditure or an individual looking to take out a loan, default probabilities are used everywhere and every day.
From children in primary school questioning whether lending your pencil to your friend is safe to now, we use these probabilities when lending money to a friend.
Unknowingly, these probabilities are elicited in our day-to-day lives by us and those around us and affect our decisions and those around us.
Despite the definition and notion being reasonably vague, we can dive in further and properly grasp the notion of default probabilities in context by understanding how they are interpreted in real-life markets.
High-Yield vs. Low-Yield Debt
Suppose we have two individuals applying for a credit card, Person A and Person B. Which application is more likely to be successful in this case? The correct answer is “No idea!” because we don’t know anything about either of them.
Now we are told Person A has a credit score of 800 with an annual income of £100,000, and contrastingly Person B has a credit score of 400 and an annual income of £18,000.
Who do you think is the creditor’s choice in this situation, and hence is most likely to have a successful application now?
We can all see that Person A should be the clear favorite in this application due to a higher income and a superior credit score. But why?
Without knowing, once we were given further information regarding the two factors of income and credit score, we all elicited respective probabilities of default in making our decision.
The fact that Person A earns more and has a better credit history would translate to a better chance that the person can keep up with payments and hence is an overall better bet for the creditor.
Moreover, in this case, Person A will have a low probability of default, regarded as favorable, and Person B will have a high likelihood of default.
Therefore, we all inherently calculate these probabilities when making decisions such as lending money. Financial markets, fixed-income markets, and governing bodies hence take this into practice at a much larger scale.
Credit Ratings and Probability of Default
Now that we have further explored the notion of default probabilities and one possible way to explore them, we can understand how they are used in the real world through credit ratings.
Credit ratings are assigned in many cases, famously through bond credit ratings used by small and large investors everywhere. Some of them are:
1. Bond Credit Ratings
In the financial world, a large variety of firms and entities take responsibility for assessing and assigning these probabilities.
Most commonly, this is done to ‘rank’ and ‘quantify’ a bond relative to riskiness. Firms assess the bond and calculate the chance the borrower will default on paying the coupons and premiums.
The main firms in charge of this process include Moody’s, S&P, and Fitch. We see that they all use different ranking systems, which one of you can look at online on their platforms.
For instance, at Moody’s, bonds are usually assigned ratings such as AAA, AA, BBB,... and so on.
AAA is the highest attainable ranking, correlated with a low probability of default. C (sometimes D) is the lowest possible rank, correlating to a high probability of default.
2. Other Ratings
Additionally, the economists and investors among us would also be familiar with credit ratings on a macroeconomic scale, which refers to ratings assigned to countries that quantify the obligor’s reliability to repay loans.
Despite discussing where and when these credit ratings are used, we have yet to discuss the methodology used in calculating these probabilities.
Calculating a Probability of Default
Continuing the discussion, we now understand how investors, banks, and other lenders calculate this probability.
1. Estimation
One method used when carrying out these calculations is using past data to estimate the probability.
This is a very effective strategy because, despite often not getting the exact probability, we can get very close to the actual figure, enough so that we can make decisions and classify the risk of default with relative ease and effectiveness.
Another advantage of this method is that it is sometimes a lot more productive, takes a lot less time, and the resources required are easily found.
Therefore, one would employ this method of calculating probabilities to find a rough figure and gauge the level of risk associated with buying a bond or approving a loan.
Carrying out the calculation requires only past data regarding the financial product or the obligor, which can usually be found quite easily through various known databases.
For example, suppose our risk-averse investor is looking to buy a bond from company X, available only till the end of the day. Our investor wants to know the chance that company X will default; hence, they want to know the chance they will make a loss on their investment.
Now the issue is the investor is running out of time to execute the buy and needs to decide with haste. What should they do?
2. Estimate
To begin, they will look to access data on the history of this particular bond (available through agencies such as Moody’s).
Using this, the investor will look at how many people have previously bought this bond and then look at how many instances there have been in which default occurred.
Then using
P = (Amount of Defaults/Amounts of Bonds sold) x 100
They have a rough probability of default of P%. i.e., depending on their level of risk aversion, they will decide if the probability will suffice and make their decision based on that.
3. Disadvantages of Estimation
As noted previously, we have seen the advantages of the estimation method in eliciting the probability of default.
In summary, estimation is very useful for effectively calculating in a hasty environment. Additionally, it provides a really good approximation of our likelihood.
However, we find this method has significant drawbacks too:
- Heavily dependent on accessible data. Data may not be easy to access in many situations, so we cannot estimate.
- For instance, if we have a newly listed security or a client with a limited borrowing history, a lack of data will lead to a very inaccurate probability, as limited data can have many variations.
Therefore, we require alternative methods to calculate the default probability.
4. Alternative Methods
Through the use of software and statistical modeling, a large range of alternative methods has been developed.
Namely, linear regression and neural networks are used in the industry to perform our required calculations.
Stressed and Unstressed Probabilities
One of the important concepts, and distinctions, to make when calculating our probability can now be explored further as we have now established methods through which these calculations are carried out.
So far, we have vaguely coined ‘factors’ that contribute to calculating our probability. Now we can begin to delve deeper.
When looking at our obligor’s probability of default, we can partition and classify our factors into two different sections:
- Macroeconomic factors- those out of the control of the borrower
- Obligor-specific factors- those in the power of the borrower.
1. Stressed Probabilities
Obtaining a default probability with macroeconomic factors at that time considered, along with obligor-specific ones, we are inherently calculating the Stressed PD for our obligor in this transaction.
This leads to the belief that if the economic climate improves, this probability will too. Inversely, if economic conditions worsen, the probability will accordingly deteriorate.
However, this correlation isn’t always intuitive and doesn’t always come to fruition. Hence, in such a situation, one may disregard macroeconomic factors entirely, giving an unstressed probability.
2. Unstressed Probabilities
Following this, we gauge that Unstressed PDs will lead to a more strict probability that will only be affected/changed if the borrower’s situation changes. Only these factors were considered in the first place.
For instance, a company’s probability of default on a loan repayment will only change if there is a change in its revenue or plenty of other factors that it can control. But, a change in inflation rates won’t affect our probability as these weren’t considered in the first place.
What are Credit Default Swaps?
Most people associate loans and other such transactions with having just two sides: The borrower and the lender.
There is another common practice in the market known as a credit swap. Not only will we have a lender and a borrower, but also a third entity involved.
It involves the loan being taken out in the borrower's name but with the agreement that this third party will cover any default. In return, the borrower will compensate the individual with an agreed-upon sum that can make this worth their while, known as a coupon.
Contextually, third-party individuals will act as a bridge between the lender and the borrower. This third entity can come from an investor or a bank.
The obligor uses a credit swap to hedge against loss associated with default as they have an additional safety blanket in the form of a tertiary investor looking to take the risk of default upon themselves.
We can now begin to explore when and why the different parties involved in this deal would find it beneficial and when it would be detrimental to them.
Advantages and Disadvantages of Credit Swaps
Now we can discuss the advantages and disadvantages of such a transaction from the viewpoint of all three parties.
1. Borrower
The main advantage of such a deal to the borrower would be that any responsibility of a default on repayment falls on the third individual, which is less detrimental to the borrower’s credit history and subsequent rating.
Additionally, the borrower would benefit if they cannot get a loan due to their credit rating; hence, introducing a proxy will help their chances of getting a loan.
On the other hand, the disadvantage to the borrower would be that if the borrower successfully pays back the entirety of the loan/doesn’t default, the borrower will still have to honor the agreement with the third party individual and hence incurs extra costs.
Therefore, such a deal will only really be beneficial for a borrower if they believe they are at risk of default or if they believe they won’t get the loan in the first place. Otherwise, such a deal will lead to unrequired losses.
2. Lender
The lender’s point of view in this transaction remains mainly unchanged as their benefit is that the default probability is compounded as it considers the borrower and the third individual.
On the other hand, the lender stands to lose very little in such a transaction. They have a better chance of being repaid and making a profit on the transaction. Hence, such a deal is sought from the lender's point of view.
3. Outside Entity
The third party in this deal will benefit from this as they have an agreement with the borrower and will somehow be getting compensated for taking on responsibility.
However, in the case of a default on the borrower's side, the individual may take a loss on the deal; the default amount, which they will have to cover, may be significantly larger than the compensation received, leading to a loss.
Therefore, we see such a deal will only be taken on from all parties if the borrower and the outside entity both see value in the deal. Thus, the borrower believes their default probability is large enough to require cover.
On the other hand, the outside entity would need to see this deal as profitable and hence will believe that their agreed-upon compensation is better than the borrower’s expected default amount.
We see that a credit swap gives us another formula for calculating a default probability.
As previously defined,
P = (Coupon Value in CDS Market/Loss given a default) x 100
In this case, the coupon value would be given to us by the market in which borrowers look to sell their credit swap. The loss given default will quantify the amount the borrower stands to lose in case they default.
Hence, we obtain P% as the probability the borrower will default. The third entity usually uses this method before buying the swap as they want to look at the profitability of this swap.
Anyone interested in further learning about the credit swap market and its effects can be found abundantly on the internet and the WSO platform.
Probability of Default FAQs
As the name suggests, a PIT probability is used to classify probabilities calculated using a short timeframe. In context, using macroeconomic or obligor’s data over the last year or less.
On the other hand, a TTC probability will take into account a longer timeframe; in theory, it takes into account a whole economic cycle (usually 4-5 years’ worth of data).
A more in-depth discussion regarding PIT and TTC probabilities and how they are used can be found on the internet.
For those interested in statistics, and familiar with expectations, we know we can now extend our concept and use this probability to calculate expected losses on a transaction such as a loan or a bond.
This will require further knowledge of a few particular variables we haven’t seen in this article. However, the conversation flows perfectly onward and can be found here.
Researched & Authored by Shaun
Free Resources
To continue learning and advancing your career, check out these additional helpful WSO resources:
or Want to Sign up with your social account?