Yield Supplement Overcollateralization (YSOC). When there is a low yielding bond, there is a goal to compensate potential investors. Thus, calculations for the difference between the value of the future scheduled cash flows at the current rate need to be made. Then the difference between the value of the future scheduled cash flows is calculated at the acceptable rate which investors would expect to receive.  

The goal is to compensate investors for this difference – (this happens frequently within the Solar field). The acceptable discount rate is called the Specific Discount Rate. 

YSOC Calculations: 

YSOC Level Pay:

  • First the loan is projected under no scenarios – base case projection of future cash flows
  • Then discount the loan at its actual rate – which will be the future scheduled payments at the loan rate
  • Then the loan is discounted at the specific rate – which will be the future scheduled payments at the specific rate
  • The difference between the two, is the YSOC for that period

YSOC:

  • Assuming that the payments are not known, from the start period which is 0, and discount the CF backwards for each term we discount it twice - once at the loan’s rate and once at the specified rate
  • The difference between the two is the YSOC for that period

Historical Loan Deal:

The YSOC Value received from the trustee can be placed in the Historical Loans on T-REX. 

  • It is not likely that YSOC will be reported by a trustee for each single loan, but will likely be aggregated for the entire pool

 

In the case that YSOC is reported granularly, T-REX has a place to plug it in under the Historical Loans tab, where the YSOC column (far right) corresponds to each loan detailed. 

Important to Note 

  • YSOC is calculated per period
  • YSOC profile is representative of YSOC for all the periods
  • YSOC is calculated on replines and not on individual loans, the loans are aggregated. This helps us calculate the YSOC dynamically. Each prepayment, each scenario changes the YSOC for the future as well
  • In order to not run the entire calculation each period, we just calculate a performing fraction and multiply the original period YSOC by the performing fraction  

The difference between YSOC and YSOC Level Pay:

The difference between YSOC and YSOC Level Pay stems from the payment method.

  • In YSOC level pay, it is assumed that there is a constant payment and equal spacing between payments, it is necessary to use the re-amortized scheduled payment method,  the constant payment that exists in the period before the re-amortization. After that period, the PMT function will run and once again receive a constant payment for each period based on the remaining balance.

Important to Note: The payment that will be received for each period is known, so the cash flows of all known future payments can be discounted and receive a present value. With this present value, it can be discounted with the existing discount rate and the specified discount rate (YSOC Level Pay). 

In YSOC, the idea is similar, the only difference is – our payments are not fixed, they may vary due to defaults and prepayments, as YSOC supports any payment method, the payments may vary between periods. If the payments are not fixed, the amount of each payment specifically for each period from the beginning is not known, the calculation must begin from period 0, and then discount backwards, once with the loan’s discount rate and then again with the specified discount rate, and then the YSOC is found. 

The only difference is the way in which the payment schedule is constructed. The idea is the same behind both, it is merely a distinction between how to build the payment schedule when the future cash flows are known, and when they are not fixed. Hence, if we use level pay payment method, both YSOC and YSOC level pay will show the same results because it enforces equal payment amount in equal spacing.

Detailed Calculation:

YSOC Level Pay

Calculate the basic PMT using the balance, interest, and principal. If necessary, include CPR and CDR scenarios (follow instructions  earlier in the document under Overview of Loans > Understanding the Calculations).

In this example we will use the following numbers:

Detailed PMT calculation:

PMT column

YSOC is calculated per payment period, we create 2 columns, 1 is the Present Value of the Loan at the Loan’s interest Rate, and the 2nd is the Present Value of the Loan at the Specified Interest Rate. 

PV at Loan’s interest rate: We begin at period 0, and discount the PMT by the Loan’s interest rate: (1951.09$*((1-(1+(3.311%/12))^(20- 0))/(3.311%/12))

The payment is multiplied by 1+ the monthly interest rate. All that is raised to the power of the remaining periods. The result is divided  by the monthly interest rate.

The calculation is applied throughout the periods.

Note: the calculation of the periods is done total period – current period so that when dragging the calculation to other periods it will  update automatically. In period 0, we raise it to the power of 20, and in period 1 to the power of 19, etc.  

Note: We calculate the interest rate by period, which is monthly, but the given interest rate is 3.311% per year, thus we divide it by 12 in  the discounting.  

Now we have the PV at the Loan’s interest rate, we move to calculate the PV at the Specified Interest Rate.  

In this case the value is 0.0475. The calculation will be exactly the same, we just change the interest rate:

Same notes hold here as well

Drag the values for the whole column.

Now to calculate the YSOC  

Add a new column called YSOC

Deduct the value of PV @ specified from PV @ loan rate> YSOC = PV@Loan rate – PV @ Specified Rate

Drag the calculation through the column

Congratulations! You’ve just calculated YSOC level pay.

Note that by going back to the original PMT, and changing CDR and CPR assumptions, the values will adjust accordingly – the YSOC is  taking into account the CPR and CDR for the future projections.

YSOC:

when calculating the YSOC, we have payments that are not equally spaced, so we cannot use the same method to calculate the PV

thus, we once again lay down the loan PMT calculations, with the different payment method (here it’s 30/360)

then we will calculate the PV, once with the Loan’s original interest rate, and once with the specified rate

this time, because the payments are unpredictable, we will start our calculation from the bottom, the last period - period 20, and set it to 0,  because everything will be paid by period 0

then we will start building the pervious period, period 19,

the PV @ loan’s rate calculation : ((sched int+sched prin period 20)+ PV @ loan’s rate period 20)/(1+Loan’s int rate*(30/360)) then the calculation for the PV @ specific rate is the same, but with the specific rate instead:

((sched int+sched prin period 20)+ PV @ specific rate period 20)/(1+specific int rate*(30/360))

the YSOC is the difference between the two then pull the calculation up.