### Author Topic: Another reason future years decline  (Read 3634 times)

#### OleBill

• Newbie
• Posts: 22
##### Another reason future years decline
« on: July 21, 2017, 05:17:59 PM »
A recent post by SeanMCA on another thread made me curious about the impact of the service charges on fully paid loans. Unfortunately, this led me down a path looking at payments made on a specific loan. I duplicated the calculations Lending Club made with each payment and realized how misleading the interest rate is. They compute the interest on the declining balance (as they should) but as the payments add up, the interest you earn declines.

I did an example starting with \$100 invested at 10%. The borrower would have to pay back about \$3.25 a month to pay this off in 36 months. Following is a chart of the first few months of payments.

Year   Month   Balance   Payment   Interest   Pd Princ   New Bal
10.00%   0   \$100.0000            \$100.0000
1   1   \$100.0000   \$3.2500   \$0.83   \$2.4167   \$97.5833
1   2   \$97.5833   \$3.2500   \$0.81   \$2.4368   \$95.1465
1   3   \$95.1465   \$3.2500   \$0.79   \$2.4571   \$92.6894
1   4   \$92.6894   \$3.2500   \$0.77   \$2.4776   \$90.2118

If you take this through the 36 months and total by year, you get the following sums.
Amt Pd   Interest   Balance   Ret/\$
Year 1   \$39.0000   \$8.6332   \$69.6332   8.63%
Year 2   \$39.0000   \$5.4534   \$36.0866   7.83%
Year 3   \$39.0000   \$1.9406   -\$0.9727   5.38%
Life   \$117.0000   \$16.0273      5.34%

You earned \$16.03 in interest on \$100 over 3 years. That is an annual return of 5,34%. If you add in the service fee (totals \$1.17), your return is further reduced to 4.95%. And, these assumptions to not consider the impact of charge offs and fully paid loans.

The only way you can continue to get near 10% is to constantly re-invest the money you receive. When you want off this merry-go-round, you will pay a penalty.

Where am I wrong?

#### AnilG

• Hero Member
• Posts: 1123
##### Re: Another reason future years decline
« Reply #1 on: July 21, 2017, 06:09:11 PM »
The keyword is amortized loans. These loans are constant repayment declining balance loans. Interest / Remaining Principal ratio stays the same during the life of loan sans default.

You can take the repayments out of account and invest anywhere else you like. There is no penalty for getting off the merry go-round. Continuous reinvesting gives appearance of higher return because repayments on newish loans mostly consist of interests and little of principal repaid. Once you reach a level reinvesting rate, you portfolio returns will level off too. San defaults, return fluctuate mostly when money is added and deployed to or cashed and withdrawn from account.

You are trying to find fault where there is none.

A recent post by SeanMCA on another thread made me curious about the impact of the service charges on fully paid loans. Unfortunately, this led me down a path looking at payments made on a specific loan. I duplicated the calculations Lending Club made with each payment and realized how misleading the interest rate is. They compute the interest on the declining balance (as they should) but as the payments add up, the interest you earn declines.

I did an example starting with \$100 invested at 10%. The borrower would have to pay back about \$3.25 a month to pay this off in 36 months. Following is a chart of the first few months of payments.

Year   Month   Balance   Payment   Interest   Pd Princ   New Bal
10.00%   0   \$100.0000            \$100.0000
1   1   \$100.0000   \$3.2500   \$0.83   \$2.4167   \$97.5833
1   2   \$97.5833   \$3.2500   \$0.81   \$2.4368   \$95.1465
1   3   \$95.1465   \$3.2500   \$0.79   \$2.4571   \$92.6894
1   4   \$92.6894   \$3.2500   \$0.77   \$2.4776   \$90.2118

If you take this through the 36 months and total by year, you get the following sums.
Amt Pd   Interest   Balance   Ret/\$
Year 1   \$39.0000   \$8.6332   \$69.6332   8.63%
Year 2   \$39.0000   \$5.4534   \$36.0866   7.83%
Year 3   \$39.0000   \$1.9406   -\$0.9727   5.38%
Life   \$117.0000   \$16.0273      5.34%

You earned \$16.03 in interest on \$100 over 3 years. That is an annual return of 5,34%. If you add in the service fee (totals \$1.17), your return is further reduced to 4.95%. And, these assumptions to not consider the impact of charge offs and fully paid loans.

The only way you can continue to get near 10% is to constantly re-invest the money you receive. When you want off this merry-go-round, you will pay a penalty.

Where am I wrong?
---
Anil Gupta
PeerCube Thoughts blog https://www.peercube.com/blog
PeerCube https://www.peercube.com

#### Fred93

• Hero Member
• Posts: 2245
##### Re: Another reason future years decline
« Reply #2 on: July 21, 2017, 06:29:54 PM »
They compute the interest on the declining balance (as they should) but as the payments add up, the interest you earn declines.

Your first mistake is to concern yourself with "interest" vs "principal" portions of each payment.  A dollar is a dollar.  You don't  care whether some calculation called it interest or principal or cheesecake.

You get the same payment every month.  If you use those payments to compute IRR, you will see what you are earning.  No problemo.

Quote
The only way you can continue to get near 10% is to constantly re-invest the money you receive.

Correct... because if you don't, then you have UNinvested money lying around.  You shouldn't expect UNinvested money to earn a return.  You fix that by buying more loans with the recycled money.

#### sensij

• Newbie
• Posts: 31
##### Re: Another reason future years decline
« Reply #3 on: July 21, 2017, 08:00:48 PM »

You can take the repayments out of account and invest anywhere else you like. There is no penalty for getting off the merry go-round. Continuous reinvesting gives appearance of higher return because repayments on newish loans mostly consist of interests and little of principal repaid. Once you reach a level reinvesting rate, you portfolio returns will level off too. San defaults, return fluctuate mostly when money is added and deployed to or cashed and withdrawn from account.

Tangentially, have you ever worked out what the weighted average age will level out to if a lump sum is invested and all repayments re-invested, if the portfolio behaves as historical averages suggest it might?

#### .Ryan.

• Jr. Member
• Posts: 84
##### Re: Another reason future years decline
« Reply #4 on: July 21, 2017, 08:23:18 PM »

Quote
The only way you can continue to get near 10% is to constantly re-invest the money you receive.

Correct... because if you don't, then you have UNinvested money lying around.  You shouldn't expect UNinvested money to earn a return.  You fix that by buying more loans with the recycled money.

Fred93, I've struggled with this, do you mind explaining it a bit more to me?

At face value, I have always taken this to be the Hotel California of P2P investment returns. If you want to keep returns decent, you need to keep re-investing. As soon as you want to take some profits off the table, your returns take a nose dive (I think most people have seen this).

In order to keep returns positive, it seems like I cant take anything out of my P2P investment. As soon as I do, my returns shit the bed. This is not the case when I divest in equities holdings.

Am I looking at return values (supplied by LC) incorrectly? What am I missing here?

Thank you!!

#### apc3161

• Newbie
• Posts: 43
##### Re: Another reason future years decline
« Reply #5 on: July 21, 2017, 10:11:20 PM »
I'll give an example to highlight the point:

Imagine there was an investment that returned 1% each day. But every single day, in the evening, they gave you all your money back. Each night, you had to decide whether or not you wanted to invest the following day.

You start off with \$100. That night, they give you \$101. You decide to re-invest and give them \$101 for the next day. At the end of the next day, they hand you \$102.01. This continues for 1 week, after which you have \$107.21. They return this money to you. This has been great, you've been having an average rate of return of 1% per day. This night however, you decide you don't want to reinvest. You do this 1 week. So after 14 days, you still have \$107.21. This means your average return over 14 days, more or less, dropped from 1% per day to 0.5% per day, solely because you stopped investing. This makes sense, if you don't invest your money, you won't make any returns, and your average rate of return decreases as time passes.

In the case of LC, it's similar to the above example, the only difference being that each night they give you back ~0.07% as opposed to 100%. If you don't re-invest what they give back to your, your average rate of return will decrease. However, the rate of return for the money that you still have invested, will remain the same.

#### AnilG

• Hero Member
• Posts: 1123
##### Re: Another reason future years decline
« Reply #6 on: July 22, 2017, 03:35:03 AM »
I haven't used the historical data to estimate age as it will be too time consuming and computing intensive if at all possible.

But I have modeled it with lot of simplifying assumptions. If you made one-time lump sum cash infusion at the start and are lending at 12% rate on first day of each month, reinvesting all monthly repayments, deposit/withdraw no cash from account and encounter no defaults, the weighted portfolio age should be about 17.4 months for 36 month loan portfolio 107 months after opening the account and about 27.5 months for 60 month loan portfolio 178 months after opening the account. In short, we are looking at a decade or more before portfolio reaches steady rate of reinvesting after large initial investment. Another way to look at it that it will take almost 3x of loan term before you reach steady reinvestment rate.

I haven't modeled it but I expect a DRIP like program to reach reinvesting steady state much quicker in my modeled scenario. Defaults are very difficult to model as timing and magnitude will change the reinvestment dollars available every month.

There may be an approximation method from the Bonds and MBS domain but I haven't looked into it.

Tangentially, have you ever worked out what the weighted average age will level out to if a lump sum is invested and all repayments re-invested, if the portfolio behaves as historical averages suggest it might?
---
Anil Gupta
PeerCube Thoughts blog https://www.peercube.com/blog
PeerCube https://www.peercube.com

#### Fred93

• Hero Member
• Posts: 2245
##### Re: Another reason future years decline
« Reply #7 on: July 22, 2017, 04:32:56 PM »
Fred93, I've struggled with this, do you mind explaining it a bit more to me?

APC3161 explained the basic idea well above.  Believe it or not, this is the main thing that confuses people.

There are some other things going on.  What happens to "your returns" depends on what you are using as "your returns".  If you're looking at the NAR or ANAR number that LC gives you, or the similar number that Prosper gives you, then there are some more considerations.  Those numbers presume that the only imparements are the ones that have already made themselves known thru default (and in the case of ANAR, delinquency).  Those numbers calculate what will happen if EVERYONE ELSE pays off as scheduled.  We all know that ain't gonna happen.  Your return in the end will be lower than ANAR.

But here's how people get confused... People who don't understand how the math works think like this:  They open an account, and then after say 3 or 4 months, they see their ANAR is 15%, and they think they are doin' really great.  However, they haven't seen ANY loans chargeoff yet.  This means that NAR is just the average interest rate on the notes in their portfolio.  Why?  It takes 5 months for a loan to charge off.  After 1 month the 1st payment is due.  After 2 months it can be 1 month late.  ... After 5 months it can be 4 months late, and after that they charge off the loan.  So at 5 months, ANAR starts coming down.  Until your portfolio matures, and becomes a mix of loans of all ages, ANAR keeps coming down.  This happens because the fraction of your loans that are <5 months old goes down.  Pretty damn simple, eh?  And yet, most people still don't get it.  This says nothing about loans, or your selection of loans.  Its just something baked into NAR and ANAR.   You can see this if you look at the "understanding your returns" page.  You see the swarm of dots representing other folks' accounts.  It comes sliding down as the average age goes up, until it about 12 months, where most portfolios are mature and therefore no longer have an excessive fraction of their loans <5 months.  This single factor is the cause of most of the notions that returns come down over time.  NAR and ANAR come down over time.  How well you're doin' really hasn't changed.

From here it gets more subtle.  A mature portfolio is a mix of all ages of loans.  A mature portfolio of 36 month loans would have an average age of 18 months if all loans lasted the full 36 months.  A lot of loans repay tho, so the average is around 12 months.  If a portfolio averages 12 month age, you can see that a significant fraction of it will be loans with <5 months age.  However, when a person stops investing, the portfolio subsequently ages another 5 months after that, now there are no new loans, so all loans are subject to possible chargeoff, so the rate of chargeoff goes up a bit, and NAR comes down a bit.

I will add that this isn't just a negative statement about NAR and ANAR.  Many other measurements of "return" exhibit this same behavior.  To get a measure of return that does not exhibit this behavior, you have to throw in an estimate of the future chargeoffs of the loans that are presently paying on schedule, ie "current".  This of course requires predicting the future, which introduces another kind of error.  I've sometimes argued that such things were the right thing to do, but I've relaxed over time.

There are other more subtle effects, but they are subtle.  Loans don't default at a uniform rate vs time.  However, that isn't as big an effect as the one above.  There are self-selection effects ... The people who stop tend to be more of the people who are not doing well, etc.

There are many other subtle effects.  You will see lots of arguments about these subtle effects.  In most of these arguments, people ignore or don't understand the  big ones listed above.

#### .Ryan.

• Jr. Member
• Posts: 84
##### Re: Another reason future years decline
« Reply #8 on: July 24, 2017, 12:09:43 AM »
Thanks for the great responses, APC, Fred93. I have definitely been looking at it wrong.

#### sensij

• Newbie
• Posts: 31
##### Re: Another reason future years decline
« Reply #9 on: July 24, 2017, 03:02:03 PM »

But here's how people get confused... People who don't understand how the math works think like this:  They open an account, and then after say 3 or 4 months, they see their ANAR is 15%, and they think they are doin' really great.  However, they haven't seen ANY loans chargeoff yet.  This means that NAR is just the average interest rate on the notes in their portfolio.  Why?  It takes 5 months for a loan to charge off.  After 1 month the 1st payment is due.  After 2 months it can be 1 month late.  ... After 5 months it can be 4 months late, and after that they charge off the loan.  So at 5 months, ANAR starts coming down.  Until your portfolio matures, and becomes a mix of loans of all ages, ANAR keeps coming down.  This happens because the fraction of your loans that are <5 months old goes down.  Pretty damn simple, eh?  And yet, most people still don't get it.  This says nothing about loans, or your selection of loans.  Its just something baked into NAR and ANAR.   You can see this if you look at the "understanding your returns" page.  You see the swarm of dots representing other folks' accounts.  It comes sliding down as the average age goes up, until it about 12 months, where most portfolios are mature and therefore no longer have an excessive fraction of their loans <5 months.  This single factor is the cause of most of the notions that returns come down over time.  NAR and ANAR come down over time.  How well you're doin' really hasn't changed.

From here it gets more subtle.  A mature portfolio is a mix of all ages of loans.  A mature portfolio of 36 month loans would have an average age of 18 months if all loans lasted the full 36 months.  A lot of loans repay tho, so the average is around 12 months.  If a portfolio averages 12 month age, you can see that a significant fraction of it will be loans with <5 months age.  However, when a person stops investing, the portfolio subsequently ages another 5 months after that, now there are no new loans, so all loans are subject to possible chargeoff, so the rate of chargeoff goes up a bit, and NAR comes down a bit.

I will add that this isn't just a negative statement about NAR and ANAR.  Many other measurements of "return" exhibit this same behavior.  To get a measure of return that does not exhibit this behavior, you have to throw in an estimate of the future chargeoffs of the loans that are presently paying on schedule, ie "current".  This of course requires predicting the future, which introduces another kind of error.  I've sometimes argued that such things were the right thing to do, but I've relaxed over time.

4 months is a nice check point since I've just passed that on my IRA account.  I struggle with the fact that none of the metrics Lending club provides seem to look at actual account balance, so I have to track that on my own.

Starting with an \$85676 deposit on Feb 17, is was \$89575 on July 17.  A \$1500 IRA promotional credit was paid into the account on July 12, so subtracting that leaves \$88075, a gain of 2399 over 4 months, or 2.8%, which annualizes out very close to the unadjusted weighted average interest rate.  (it will be harder to adjust for the promotion later, as the notes it purchased start to contribute to repayments, defaults, etc.).

Illustrating Fred93's point, although the IGP notes aren't contributing to re-payment, they still contribute their face value to the balance, so some sort of adjustment looks called for.  I understand the path that leads one to using metrics of cash flow (payments received vs defaults booked) as an indicator of account health.

I haven't used the historical data to estimate age as it will be too time consuming and computing intensive if at all possible.

But I have modeled it with lot of simplifying assumptions. If you made one-time lump sum cash infusion at the start and are lending at 12% rate on first day of each month, reinvesting all monthly repayments, deposit/withdraw no cash from account and encounter no defaults, the weighted portfolio age should be about 17.4 months for 36 month loan portfolio 107 months after opening the account and about 27.5 months for 60 month loan portfolio 178 months after opening the account. In short, we are looking at a decade or more before portfolio reaches steady rate of reinvesting after large initial investment. Another way to look at it that it will take almost 3x of loan term before you reach steady reinvestment rate.

Thank you...  logic suggests the long term average age would be about half the average weighted term, shortened by pre-pays and defaults.  The cynic in me sees something of a minimum at around 13 months in the "Understanding My Returns" scatter plot, so I am guessing with no support that the 17.4 months you calculate would shorten to something closer to 13 months when the assumptions are relaxed (consistent with what Fred93 wrote).  I'm a little surprised it takes almost 10 years to reach stability....

#### LC_SinkingShip

• Newbie
• Posts: 1
##### Re: Another reason future years decline
« Reply #10 on: July 24, 2017, 03:43:42 PM »
You're not wrong. The way they calculate and post returns is a total joke. If you also factor in the taxes and or fees you will have to pay when you go to file at the end of the year, and or the fees at SDIRA to close your account. You will absolutely be in the negative.

#### AnilG

• Hero Member
• Posts: 1123
##### Re: Another reason future years decline
« Reply #11 on: July 25, 2017, 02:29:34 AM »
The weighted average portfolio age is only calculated for active notes, i.e. the loans that have not defaulted or fully paid. So the calculations are only weighing active notes and premature defaults and prepayments may have little impact on the portfolio age, most probably timing of defaults and prepayment have more impact.

After plotting the portfolio age with months, I realized the portfolio age reaches a plateaus pretty quickly once initial loans have matured. So I need to correct my earlier interpretation that it may take over a decade. It looks like we might reach ~17 months portfolio age plateau for 36 month loans by ~72 months and reach ~27 month portfolio age plateau for 60 month loans by ~120 months in the model constructed under assumptions as mentioned before. Basically 2x term may be a good rule of thumb. See the attached portfolio age charts for both 36 and 60 months portfolio.

Thank you...  logic suggests the long term average age would be about half the average weighted term, shortened by pre-pays and defaults.  The cynic in me sees something of a minimum at around 13 months in the "Understanding My Returns" scatter plot, so I am guessing with no support that the 17.4 months you calculate would shorten to something closer to 13 months when the assumptions are relaxed (consistent with what Fred93 wrote).  I'm a little surprised it takes almost 10 years to reach stability....
---
Anil Gupta
PeerCube Thoughts blog https://www.peercube.com/blog
PeerCube https://www.peercube.com