This post describes an approach to measuring the exposure profile and adjusted returns of a MakerDao CDP. A separate post will provide a quantitative approach and an example calculation of the spreads described below.

What is a risk spread/premium and why is it relevant for the MakerDao sysem?

The MakerDao Dai Stability Fee is the cost of capital for a Dai borrower and it is also the compensation that a lender receives for extending a loan via the CDP. While a MakerDao loan is very safe, it is not risk free. To measure the additional compensation that a lender receives for extending risky debt relative the compensation that they could receive by extending risk-free credit, financial analysis commonly uses a benchmark-spread metric (Z-spread, credit spread, etc.).

Today, there is no real risk-free lending rate for decentralized assets. Despite the high collateral ratio and on-chain nature of CDP contracts it is possible that the CDP borrower defaults and the collateral liquidation proceeds do not cover the debt amount. This is an exposure to the MakerDao system generally — with Single-Collateral Dai loans it is an exposure to PETH holders, while with the current design for Multi-Collateral Dai it will be an exposure to all MKR holders. (note: editing/further explanation needed)

Because a CDP is a risky instrument, it is appropriate to consider the debt yield (i.e. Stability Fee) as a spread to a theoretical risk-free interest rate, though a spread could also be calculated for benchmarks other than a risk-free rate (DIPOR, for example). This theoretical spread measures the compensation to Dai lenders above or below the benchmark, and it is an important metric for any risk-reward framework.

As the MakerDao and Dai lending ecosystem evolves, risk-adjusted returns will become increasingly important for evaluating the risk-reward relationship of CDP loans, and should serve as a analytical tool for future decisions with respect to Risk Parameters and monetary policy decisions. Observing and reacting to changes in risk-adjusted returns can be used to evaluate the impact of market forces other than the risk of bad debt. This can also serve as means of more accurately comparing lending rates across platforms.

Certain features of a MakerDao CDP introduce complexities to the calculation of spreads to a benchmark. The liquidation process, for example, should be treated differently than the maturity of a traditional fixed-term loan. The variable Stability Fee, auction process, and ability to add or remove collateral also complicate the comparison of a Dai loan to a theoretical fixed-term risk-free rate. Despite these complexities, we can make some simplifying assumptions to calculate various CDP risk metrics as a means of determining the risk-adjusted return of Dai-CDP loan.

What are some examples of option-based risk adjusted returns?

Traditional fixed-income markets rely heavily on spread calculations, and the US mortgage market in particular makes extensive use of spreads to measure the return of extending credit for home borrowing versus the return for lending to the US Treasury. In many cases, mortgages are guaranteed by the federal government by way of the agency securitization process, which makes it equivalent in many ways to risk-free debt, though it is different from a benchmark risk-free Treasury bond in one important respect.

Mortgages are generally pre-payable at any time. This feature means that a borrower has a right to repay the loan if better offers become available elsewhere, if the borrower sells the home, etc. This option to repay/refinance is effectively a call option on interest rates, though the borrower may not always act in economically rational manner.

By treating the borrower’s refinancing option as a call option on interest rates, one can treat the lender’s exposure profile for a federally guaranteed mortgage as a [long risk-free debt +short call option]. This framework then allows one to measure the value of the lender’s short-option position, and subtract this option value from the lender’s overall return. This yields a metric referred to as the Option-Adjusted Spread. For more information on the US mortgage market and calculating Option-Adjusted Spreads, see notes at the bottom of the page.

How can we apply the concept of an Option-Adjusted Spread to MakerDao CDPs?

A MakerDao CDP is similar to a mortgage in that its exposure profile can also be treated as a [long risk-free debt + short put option position]. Due to the collateralized nature of the CDP, there is effectively no “credit risk”. There is, however, price risk of the underlying collateral in a liquidation scenario. This risk to a downward move in price resembles is what can be described using a short-put option position. We therefore need to measure the exposure profile of this option position in order to accurately quantify the CDP’s expected exposure profile as whole. This analysis relies on the financial theory that the expected exposure of an option position is equal to its price (source). This allows us to use an option pricing model to quantify this component of the CDP’s exposure.

Using the theory that an option position’s expected exposure is equal to its price, we can also subtract the option’s value from the CDP’s return to lenders (i.e. Stability Fee), in order to quantify the Risk-Adjusted Stability Fee of the CDP.

Stability Fee = Risk-Free Benchmark + Risk-Adjusted Spread

Risk Adjusted Spread = Stability Fee — Option Value