Post by chris on Oct 8, 2014 17:01:02 GMT
I've faced some criticism for a recent change to the loan model so I thought it best to explain what happened and how it's now been resolved, and to reach as wide an audience as possible I've created a new thread. Hopefully this will also consolidate discussion into one place.
We've recently moved from a loan model where repayments used to be calculated at the loan part level to a new model where repayments are calculated at a loan level. This makes changing the repayment schedule, such as in a refinance or default situation, much easier. Coupled to this we have a much more powerful system for defining the shape of the repayments throughout the life of the loan.
One of the problems all sites face is with regards to how to round calculations to whole pence. An interest calculation or principal repayment is rarely accurate to the penny, particularly with arbitrary sizes of loan unit. Therefore at some point what is displayed to the end user needs to be rounded to a whole penny. The change in model has necessitated a change in the rounding we apply and the point at which it is applied.
Previously each loan unit tracked the total principal outstanding, and had a pre-calculated repayment schedule on a per loan unit basis that paid back both the interest and principal over time. This was calculated to 20 decimal places with each individual payment rounded down to the penny. As each principal payment came in the principal remaining against each loan unit was decreased by this rounded down figure.
The new loan model works at the loan level and is dynamically calculated so principal and interest repayments are calculated on the whole loan and then distributed proportionately to each lender. Instead of rounding down to the penny lenders are now paid to the full 20 decimal places, although on the statement this is rounded down to the penny. If you receive two repayments of 0.5p then previously the system would have held those funds and added them on to the next repayments, now they'll be in your account and add up to a penny in your balance although the statement shows both as 0p.
This change has had a knock on effect on the principal remaining shown for each loan unit. Previously because a rounded down figure was subtracted from the principal remaining it had the effect of always rounding the principal remaining up to a whole penny. The actual recalculation behind the scenes used the true figure but the principal remaining was overstated to the lenders.
The new model allows us to calculate the true figure, and as is consistent with the rest of the site we were rounding down the amount of principal displayed. This however has ended up being a change to the previous system leading some lenders to worry that we've lost some of their principal or that we've removed funds from their account.
Neither is true - the old system over reported your principal and the new system under reported it, but in both cases this was for display purposes only. The true figure has always been used behind the scenes so the change in display would have had no effect on the returns to lenders. Indeed the new system actually puts more money in your hands and allows for the accumulation of part pennies across all your loan units giving you access to those funds.
There was one unintended change and that was to the resale value on the aftermarket. Previously the principal remaining figure was in effect rounded up inflating the sale price of the loan unit, and our change reduced it by 1p.
In light of this, and to move the system back to reporting figures consistently with the old way of calculating things, I've changed the system to round the principal remaining figure up to a whole penny. This will have no effect on repayments or any part of the system except the aftermarket. In general when you are buying a loan unit you are overpaying by a fraction of a penny for that loan unit. This change restores that principle.
There is still a dilemma over how to best show the workings of the site to the lenders. Everywhere a figure is displayed either to whole pounds or whole pence there is rounding taking place, and this can have some unintended side effects such as those discussed above. Historically we've always had a principle of rounding down, however that in itself is in effect hiding information from users. What I'm thinking of doing is continuing with this practice, with the exception of the principal remaining figure which will continue to round up, but offering a rollover where if you move your mouse over the figure and leave it there a small tooltip / popup will show the true figure to 20 decimal places. This doesn't help people using touch screens / mobile, but should offer a more accurate representation to those who are interested and wish to understand why a figure they're seeing isn't as they expect.
It probably bears repeating that all sites that display figures to penny accuracy are either employing rounding or are actually only calculating your repayments to that accuracy. Others may be using floating point calculations which have statistically significant errors, rather than the fixed precision arithmetic we employ. Behind the scenes every calculation is carried out to at least 20 decimal places, and in many places it's 40 decimal places, guaranteeing that any rounding or truncating is statistically insignificant.
I'm happy to discuss any part of the system in depth if there are any further questions or thoughts on the policies I've laid out. I'd also welcome any other ideas for displaying the more precise figures to lenders without overwhelming them with long numbers.
We've recently moved from a loan model where repayments used to be calculated at the loan part level to a new model where repayments are calculated at a loan level. This makes changing the repayment schedule, such as in a refinance or default situation, much easier. Coupled to this we have a much more powerful system for defining the shape of the repayments throughout the life of the loan.
One of the problems all sites face is with regards to how to round calculations to whole pence. An interest calculation or principal repayment is rarely accurate to the penny, particularly with arbitrary sizes of loan unit. Therefore at some point what is displayed to the end user needs to be rounded to a whole penny. The change in model has necessitated a change in the rounding we apply and the point at which it is applied.
Previously each loan unit tracked the total principal outstanding, and had a pre-calculated repayment schedule on a per loan unit basis that paid back both the interest and principal over time. This was calculated to 20 decimal places with each individual payment rounded down to the penny. As each principal payment came in the principal remaining against each loan unit was decreased by this rounded down figure.
The new loan model works at the loan level and is dynamically calculated so principal and interest repayments are calculated on the whole loan and then distributed proportionately to each lender. Instead of rounding down to the penny lenders are now paid to the full 20 decimal places, although on the statement this is rounded down to the penny. If you receive two repayments of 0.5p then previously the system would have held those funds and added them on to the next repayments, now they'll be in your account and add up to a penny in your balance although the statement shows both as 0p.
This change has had a knock on effect on the principal remaining shown for each loan unit. Previously because a rounded down figure was subtracted from the principal remaining it had the effect of always rounding the principal remaining up to a whole penny. The actual recalculation behind the scenes used the true figure but the principal remaining was overstated to the lenders.
The new model allows us to calculate the true figure, and as is consistent with the rest of the site we were rounding down the amount of principal displayed. This however has ended up being a change to the previous system leading some lenders to worry that we've lost some of their principal or that we've removed funds from their account.
Neither is true - the old system over reported your principal and the new system under reported it, but in both cases this was for display purposes only. The true figure has always been used behind the scenes so the change in display would have had no effect on the returns to lenders. Indeed the new system actually puts more money in your hands and allows for the accumulation of part pennies across all your loan units giving you access to those funds.
There was one unintended change and that was to the resale value on the aftermarket. Previously the principal remaining figure was in effect rounded up inflating the sale price of the loan unit, and our change reduced it by 1p.
In light of this, and to move the system back to reporting figures consistently with the old way of calculating things, I've changed the system to round the principal remaining figure up to a whole penny. This will have no effect on repayments or any part of the system except the aftermarket. In general when you are buying a loan unit you are overpaying by a fraction of a penny for that loan unit. This change restores that principle.
There is still a dilemma over how to best show the workings of the site to the lenders. Everywhere a figure is displayed either to whole pounds or whole pence there is rounding taking place, and this can have some unintended side effects such as those discussed above. Historically we've always had a principle of rounding down, however that in itself is in effect hiding information from users. What I'm thinking of doing is continuing with this practice, with the exception of the principal remaining figure which will continue to round up, but offering a rollover where if you move your mouse over the figure and leave it there a small tooltip / popup will show the true figure to 20 decimal places. This doesn't help people using touch screens / mobile, but should offer a more accurate representation to those who are interested and wish to understand why a figure they're seeing isn't as they expect.
It probably bears repeating that all sites that display figures to penny accuracy are either employing rounding or are actually only calculating your repayments to that accuracy. Others may be using floating point calculations which have statistically significant errors, rather than the fixed precision arithmetic we employ. Behind the scenes every calculation is carried out to at least 20 decimal places, and in many places it's 40 decimal places, guaranteeing that any rounding or truncating is statistically insignificant.
I'm happy to discuss any part of the system in depth if there are any further questions or thoughts on the policies I've laid out. I'd also welcome any other ideas for displaying the more precise figures to lenders without overwhelming them with long numbers.
