How much down payment?

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iamspartacus
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How much down payment?

Post by iamspartacus »

We bought a home for ~$3M, our first home purchase. Trying to decide exactly how much down payment to make.
The standard Bogleheads advice is always pay 20%. Here's how my situation is different:

- Can pay up to 2M liquidating stocks and bonds with no cap gains consequences
- Net worth of ~6.3M across cash, bonds, stocks and retirement accounts. Enough cushion to make a bigger downpayment
- Current interest rates are quite high - 5.5%

Other factors
- Early 40s, single earner. Annual comp ~$1.5M
- We save ~450K per year
- One child in elementary school, with 200K in 529 accounts
- Marginal income tax rate of ~50% (37% Federal, 12.3% State)
- Marginal capital gains tax rate of ~37% (25% Federal, 12.3% State)

Here's my current thinking. Is this right?

I can invest cash in S&P500, or pay down my mortgage.

Paying down mortgage
- First 750K of mortgage is at effective rate of ~3.6% after mortgage tax deduction (after accounting for the standard deduction).
This is same as getting a risk-free before tax return of 5.7% on the money

- After that, mortgage is at 5.5%
This is same as getting a risk-free before tax return of 8.7% on the money

Buying S&P500
Say, expected before tax return of 8%

Conclusion
I would choose a risk-free return of 8.7% over S&P 500. So pay down till mortgage is 750K
Beyond that, not clear. Risk free return of 5.5%, or risky return of 8% - depends on risk aversion.

But paying down mortgage till 750K seems clear.

Is this right?
Last edited by iamspartacus on Thu Jun 01, 2023 3:41 am, edited 1 time in total.
secondcor521
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Re: How much down payment?

Post by secondcor521 »

iamspartacus wrote: Wed May 31, 2023 10:14 pm - First 750K of mortgage is at effective rate of ~3.6% after mortgage tax deduction (after accounting for the standard deduction).
This is same as getting a risk-free after tax return of 5.7% on the money

- After that, mortgage is at 5.5%
This is same as getting a risk-free after tax return of 8.7% on the money

[...]

Is this right?
I agree you should look at the risk-adjusted after tax rates of return.

But I don't understand the logic of grossing up the mortgage rates from 3.6%/5.5% to 5.7%/8.7%. To me, paying down a mortgage at 5.5% represents a 5.5% risk-free after-tax rate of return.

You can then take your alternative S&P500 which maybe is 11% and reduce that by taxes and then make some sort of adjustment downward for risk.

You still might choose 5.5% risk free after tax vs. whatever S&P500 number you end up with. Right now with the stock market having not done well for a year or two I know a lot of people are making that choice. I personally would look at it over the timeframe of the mortgage (30 years?) and make a decision and then stick with that strategy through the ups and downs of the market hoping for things to average out the way I think they would.

Another thing people have noted is that paying down a mortgage (or putting down a larger down payment) is a bit like a bond, so if you had any bonds in taxable paying less than 5.5% (which is probably most or all of them ;) ) it would be rational to consider shifting those assets out of bonds and into your mortgage after considering any tax consequences.

With a marginal income tax rate that high, I assume you're maxxing out any deferred compensation / 401(k)-style plans that you have available to you. Those would seem even better than taxable S&P500 and better than paying down the mortgage.
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grabiner
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Re: How much down payment?

Post by grabiner »

secondcor521 wrote: Thu Jun 01, 2023 1:41 am But I don't understand the logic of grossing up the mortgage rates from 3.6%/5.5% to 5.7%/8.7%. To me, paying down a mortgage at 5.5% represents a 5.5% risk-free after-tax rate of return.
Grossing up would make sense if the alternative investment were taxable bonds. If you buy a taxable bond yielding 5.5% and have a tax-deductible mortgage at 5.5%, you break even because both investments earn 3.6% after tax.

However, in this high a tax bracket, the alternative investment is not taxable bonds. A more fair comparison is long-term municpal bonds. Vanguard Long-Term Tax-Exempt Admiral yields 3.73% for a low-risk long-term return. Therefore, paying down a mortgage at 3.6% after tax is not worthwhile, since you can earn more on munis and keep liquidity.
Another thing people have noted is that paying down a mortgage (or putting down a larger down payment) is a bit like a bond, so if you had any bonds in taxable paying less than 5.5% (which is probably most or all of them ;) ) it would be rational to consider shifting those assets out of bonds and into your mortgage after considering any tax consequences.
And you get the same benefit if you have bonds in your IRA/401(k). If you are considering investing in stock rather than paying down the mortgage, you could instead pay down the mortgage and move an equal amount in your IRA from bonds to stock. You would be giving up the tax-free return of the bonds, but you would be gaining the tax-free return of stocks, which is significantly higher than the return on stocks in a taxable account, and you would be taking the same additional stock-market risk. (It doesn't matter much for this discussion whether the IRA is traditional or Roth. If you have a $100K IRA and will withdraw from it at a 25% tax rate, then you own $75K tax-free and the IRS and state own the other $25K. Your 75% of the IRA grows tax-free whatever you invest it in.)
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Re: How much down payment?

Post by train12 »

Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
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Re: How much down payment?

Post by grabiner »

train12 wrote: Sat Jun 03, 2023 11:32 pm Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
If you do this, you could take out an $850K jumbo loan, then pay it down to $750K quickly. Even if your lender won't let you do an immediate recast (keeping the term the same by lowering the monthly payments), you get a very good return on the $100K paydown.
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Re: How much down payment?

Post by Fat-Tailed Contagion »

Is the $1.5 M salary pre or post taxation?

Very large difference if you have $1.5 M annual to spend on consumption (+ investments) or just $750 k.

With the higher rate mortgage, I'd say go 50/50 on it. Pay down 50% and finance 50%.
“The intelligent investor is a realist who sells to optimists and buys from pessimists.” | ― Benjamin Graham, The Intelligent Investor (75/25 - 50/50 - 25/75)
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Re: How much down payment?

Post by YeWill »

Fat-Tailed Contagion wrote: Sun Jun 04, 2023 9:02 am Is the $1.5 M salary pre or post taxation?

Very large difference if you have $1.5 M annual to spend on consumption (+ investments) or just $750 k.

With the higher rate mortgage, I'd say go 50/50 on it. Pay down 50% and finance 50%.
Marginal tax rate != Effective tax rate.
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Watty
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Re: How much down payment?

Post by Watty »

iamspartacus wrote: Wed May 31, 2023 10:14 pm - After that, mortgage is at 5.5%
This is same as getting a risk-free before tax return of 8.7% on the money
It is a bit more complicated than that because you also have a sequence of returns risk so that you could get an average investing return of over 8.7% over the next 30 years and still not break even if you get unlucky and get some bad investing years early in the mortgage.

Here is a very simplistic example of that which I wrote up when interest rates were lower. It would be good to play with your actual numbers looking at it this way.
If you do not pay it off then you will have more sequence of returns risk. For example in rough numbers if you just kept a $100K mortgage and also put $100K into a separate investing account which you also pay a $500 a month mortgage out of then;

a) If you get unlucky and get a modest 10% decline in the portfolio the first year then it would be down to $90K
b) You would also need to pay the $500 a month mortgage($6,000) so your portfolio would be down to $84K
c) To pay off the mortgage at the end of the second year you would need about $96.5K so you would need to gain back $12.5K and another $6,000 for the next years mortgage payments which combined is $18.5K. That would take a 22% return on the remaining $84K to get back to the point where you could pay off the mortgage.

In the past portfolios have declined in roughly one of four or five years depending on the asset allocation. (20 to 25 percent of the time)

https://investor.vanguard.com/investing ... allocation

The sequence of returns risk can also go the other way and you could get lucky and have the first couple of years get good returns that would put you on the path for large gains over the years. There will sometimes be very optimistic projections on just how much better not paying off the mortgage could be but one limiting factor that needs to be considered is that few people actually keep a 30 year mortgage for the full 30 years. It is difficult to put a number on it but many people who own a home will sell it in less than 10 years.
Getting a higher investment return is harder than it sounds. I would pay if off quickly and not even keep the $750K mortgage for the long term. If you borrow the money and invest it and things go well and get an extra 1% after taxes that is only $7,500 a year and it will be less each year as the mortgage is paid down. In your situation that really does not "move the needle" and depending on how the money is invested you could end up in some sort of Murphy's Law situation.
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Re: How much down payment?

Post by katnok »

grabiner wrote: Sun Jun 04, 2023 8:09 am
train12 wrote: Sat Jun 03, 2023 11:32 pm Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
If you do this, you could take out an $850K jumbo loan, then pay it down to $750K quickly. Even if your lender won't let you do an immediate recast (keeping the term the same by lowering the monthly payments), you get a very good return on the $100K paydown.
Curious, why 850k instead of 750k to begin with?
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Re: How much down payment?

Post by toddthebod »

katnok wrote: Sun Jun 04, 2023 10:03 am
grabiner wrote: Sun Jun 04, 2023 8:09 am
train12 wrote: Sat Jun 03, 2023 11:32 pm Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
If you do this, you could take out an $850K jumbo loan, then pay it down to $750K quickly. Even if your lender won't let you do an immediate recast (keeping the term the same by lowering the monthly payments), you get a very good return on the $100K paydown.
Curious, why 850k instead of 750k to begin with?
The answer is literally in the post you quoted.
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Re: How much down payment?

Post by katnok »

toddthebod wrote: Sun Jun 04, 2023 10:13 am
katnok wrote: Sun Jun 04, 2023 10:03 am
grabiner wrote: Sun Jun 04, 2023 8:09 am
train12 wrote: Sat Jun 03, 2023 11:32 pm Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
If you do this, you could take out an $850K jumbo loan, then pay it down to $750K quickly. Even if your lender won't let you do an immediate recast (keeping the term the same by lowering the monthly payments), you get a very good return on the $100K paydown.
Curious, why 850k instead of 750k to begin with?
The answer is literally in the post you quoted.
I get that, but if you can get a jumbo loan and mortgage interest deduction both at 750k, why put in 850k and then pay down 100k quickly?
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Re: How much down payment?

Post by toddthebod »

katnok wrote: Sun Jun 04, 2023 1:42 pm
toddthebod wrote: Sun Jun 04, 2023 10:13 am
katnok wrote: Sun Jun 04, 2023 10:03 am
grabiner wrote: Sun Jun 04, 2023 8:09 am
train12 wrote: Sat Jun 03, 2023 11:32 pm Something else to consider in your analysis is that getting your mortgage to Jumbo loan can improve the interest rate compared to a conforming loan. In some counties, the Jumbo loan starts beyond 750k, so it might be worth it even despite the additional mortgage interest beyond 750k being not tax-deductible.
If you do this, you could take out an $850K jumbo loan, then pay it down to $750K quickly. Even if your lender won't let you do an immediate recast (keeping the term the same by lowering the monthly payments), you get a very good return on the $100K paydown.
Curious, why 850k instead of 750k to begin with?
The answer is literally in the post you quoted.
I get that, but if you can get a jumbo loan and mortgage interest deduction both at 750k, why put in 850k and then pay down 100k quickly?
I assume the $850,000 was a hypothetical amount that was above a theoretical jumbo loan limit. As in, "for example, if the jumbo loan limit is $850,000, you can take out a loan for $850,000 then pay it down to $750,000."
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Re: How much down payment?

Post by iamspartacus »

Gosh, first thank you all of you for the insightful comments.
Taking them one-by-one
secondcor521 wrote: Thu Jun 01, 2023 1:41 am I agree you should look at the risk-adjusted after tax rates of return.

But I don't understand the logic of grossing up the mortgage rates from 3.6%/5.5% to 5.7%/8.7%. To me, paying down a mortgage at 5.5% represents a 5.5% risk-free after-tax rate of return.

You can then take your alternative S&P500 which maybe is 11% and reduce that by taxes and then make some sort of adjustment downward for risk.

Sure, that works too.

When comparing an after tax return A with a before tax return B, we can either:
1. Gross up A to a before tax return A'
2. Gross down B to an after tax return B'

Isn't it the same?
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iamspartacus
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Re: How much down payment?

Post by iamspartacus »

grabiner wrote: Thu Jun 01, 2023 11:45 pm However, in this high a tax bracket, the alternative investment is not taxable bonds. A more fair comparison is long-term municpal bonds. Vanguard Long-Term Tax-Exempt Admiral yields 3.73% for a low-risk long-term return. Therefore, paying down a mortgage at 3.6% after tax is not worthwhile, since you can earn more on munis and keep liquidity.
Great point on liquidity premium - I should be willing to settle for a lower return with liquid money instead of a higher implied return of paying down mortgage but not having liquid access to home equity.

Perhaps ST CA Munis are a better benchmark? LT munis have duration risk (Vanguard LT Tax exempt fell ~20% from Dec 2021 to Oct 2022), and have to pay CA tax on it. I live in California.

Another good benchmark may be after tax return on ST Treasuries.

- ST CA Munis yield 2.85%, which is 2.48% after CA tax adjustment
- ST Treasuries yield ~5%, which is 2.95% at 41% marginal Federal tax rate

Summary: what do I prefer between 2.95% return with liquidity or 3.6% return without liquidity?
If the former, don't pay down mortgage beyond 750K, instead buy ST Treasuries
If the latter, pay down mortgage to 0.

Is this rational?
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Re: How much down payment?

Post by iamspartacus »

Fat-Tailed Contagion wrote: Sun Jun 04, 2023 9:02 am Is the $1.5 M salary pre or post taxation?

Very large difference if you have $1.5 M annual to spend on consumption (+ investments) or just $750 k.

With the higher rate mortgage, I'd say go 50/50 on it. Pay down 50% and finance 50%.
The 1.5M is before tax
Could you help me understand the 50/50 argument?
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Re: How much down payment?

Post by grabiner »

iamspartacus wrote: Sun Jun 04, 2023 4:08 pm
grabiner wrote: Thu Jun 01, 2023 11:45 pm However, in this high a tax bracket, the alternative investment is not taxable bonds. A more fair comparison is long-term municpal bonds. Vanguard Long-Term Tax-Exempt Admiral yields 3.73% for a low-risk long-term return. Therefore, paying down a mortgage at 3.6% after tax is not worthwhile, since you can earn more on munis and keep liquidity.
Great point on liquidity premium - I should be willing to settle for a lower return with liquid money instead of a higher implied return of paying down mortgage but not having liquid access to home equity.

Perhaps ST CA Munis are a better benchmark? LT munis have duration risk (Vanguard LT Tax exempt fell ~20% from Dec 2021 to Oct 2022), and have to pay CA tax on it. I live in California.
Long-term bonds are the correct comparison, because paying down a mortgage gives a fixed-dollar benefit years in the future, just as buying a long-term bond does. If you have 10 years left on your mortgage, you get the same dollar benefit in the same year by paying down the mortgage to 9 years, or by buying a 10-year bond which covers the last year's mortgage payments. Therefore, if the after-tax bond yield is equal to the mortgage rate, you might as well buy the bond and keep liquidity.

You don't have to buy this specific bond, but it gives the most fair comparison. If you choose to invest in shorter-term bonds, or lower-quality bonds, you are getting the same cost or benefit as buying this specific bond, and then a fair trade-off between return and risk.

So, if you live in CA, the best comparison is Vanguard Long-Term CA Tax-Exempt, because that gives you a low-risk long-term return exempt from CA and federal tax.

This was the type of comparison I used when I decided whether to pay off my mortgage. I live in a state with no low-cost fund, and paying off my 9-year mortgage had a 4.5 year duration, so the fair comparison is between the return on a mortgage payoff versus the after-state-tax return on Vanguard Intermediate-Term Tax-Exempt which had a 4.5-year duration at the time. In 2019, there wasn't enough of an advantage to make it worthwhile; in 2020, the extra 0.6% return on the mortgage payoff was a net benefit, so I paid it off.
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Re: How much down payment?

Post by iamspartacus »

Watty wrote: Sun Jun 04, 2023 9:44 am
iamspartacus wrote: Wed May 31, 2023 10:14 pm - After that, mortgage is at 5.5%
This is same as getting a risk-free before tax return of 8.7% on the money
It is a bit more complicated than that because you also have a sequence of returns risk so that you could get an average investing return of over 8.7% over the next 30 years and still not break even if you get unlucky and get some bad investing years early in the mortgage.

For example in rough numbers if you just kept a $100K mortgage and also put $100K into a separate investing account which you also pay a $500 a month mortgage out of then
Thank you, this is a really good mental model.
You added a liability matching component - the mortgage interest must come out of the same 100K, every year. Somewhat similar to why the safe withdrawal rate at retirement is much lower than the expected portfolio return, to address sequence of return risk.

Maybe we can formalize this as:
- I have a fixed liability stream: 5.5% interest rate every year for 30 years, and 100K lump sum at the end (assume interest-only mortgage to keep the mental model simple)
- I have 100K to fund this liability stream
- Goal: maximize after-tax money left over at the end of 30 years while minimizing probability of going broke

Options:
1. Pay 100K mortgage upfront. Money left at the end = $0. Probability of going bust = 0
2. Buy 100K of stocks. Money left at the end > $0 if stocks return more than 8.7%. But even if stocks return more than 8.7%, some probability of going broke.
3. Portfolio. Pay down x% of mortgage, leave 100-x in stocks. Reallocate every year. Likely, as we get closer to 30 years, pay more and more of the mortgage

Even without running any simulations, my intuition is that with (3), any reasonable p(going bust) wiil say x = 100%.

Thoughts?

Watty wrote: Sun Jun 04, 2023 9:44 am If you borrow the money and invest it and things go well and get an extra 1% after taxes that is only $7,500 a year and it will be less each year as the mortgage is paid down. In your situation that really does not "move the needle" and depending on how the money is invested you could end up in some sort of Murphy's Law situation.
Good point, but perhaps shouldn't look at $$ per year, but look at the extra $$ left over at the end of 30 years, including compounding?
E.g., making a good decision here with compounding could be enough to buy my daughter a house in 30 years.
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Re: How much down payment?

Post by Watty »

iamspartacus wrote: Sun Jun 04, 2023 4:47 pm Early 40s
....
Thoughts?
One of the basic rules of deciding how much risk to take is determine if you have a need to take additional risk. You clearly do not have any need to take additional risk by using a mortgage to leverage your investments.

I do not know where they draw the official line but you are on the brink of getting into middle age if you are not already there. You also just bought a house that worth half your net worth. You can afford the house but it does change your financial situation significantly so you may want to be investing a bit more defensively now.

You seem to be focused on if keeping a $750K mortgage(or whatever you decide) is a good bet or not.

That is the wrong question though and you should be asking yourself if you should be making $750K bets at this stage in life.
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Re: How much down payment?

Post by secondcor521 »

iamspartacus wrote: Sun Jun 04, 2023 3:38 pm Gosh, first thank you all of you for the insightful comments.
Taking them one-by-one
secondcor521 wrote: Thu Jun 01, 2023 1:41 am I agree you should look at the risk-adjusted after tax rates of return.

But I don't understand the logic of grossing up the mortgage rates from 3.6%/5.5% to 5.7%/8.7%. To me, paying down a mortgage at 5.5% represents a 5.5% risk-free after-tax rate of return.

You can then take your alternative S&P500 which maybe is 11% and reduce that by taxes and then make some sort of adjustment downward for risk.

Sure, that works too.

When comparing an after tax return A with a before tax return B, we can either:
1. Gross up A to a before tax return A'
2. Gross down B to an after tax return B'

Isn't it the same?
I also think you should account for risk in a similar fashion - either gross up the risk-free option by some risk factor, or gross down the risk-carrying option by that same risk factor.

As long as you're consistent and address both risk and taxes, yes, I think the two approaches are equivalent.

Personally I do the "gross down" method, but that's just my preference.
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Re: How much down payment?

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Pay as much as you can and are comfortable with
Peace of mind is important
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Re: How much down payment?

Post by goodenyou »

I am going through this same process. The friction costs of financing and the theoretical marginal benefit of “investing the rest” has me paying cash. Not even taking a construction loan to build the house. A bit older and winding down our careers into our pre-retirement phase. Haven’t had a mortgage in 10 years. No regrets. Same Federal bracket as OP and no state income taxes.
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Re: How much down payment?

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How stable and secure is the income?
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Re: How much down payment?

Post by Fat-Tailed Contagion »

iamspartacus wrote: Sun Jun 04, 2023 4:10 pm
Fat-Tailed Contagion wrote: Sun Jun 04, 2023 9:02 am Is the $1.5 M salary pre or post taxation?

Very large difference if you have $1.5 M annual to spend on consumption (+ investments) or just $750 k.

With the higher rate mortgage, I'd say go 50/50 on it. Pay down 50% and finance 50%.
The 1.5M is before tax
Could you help me understand the 50/50 argument?
Sort of a Minimize Regret strategy.

Instead on paying off all of the higher rate portion of the mortgage, pay off 50% of it and keep 50% of it financed.

In the case that your investments make 10%+ you win. If less than 8% you lose but it's not going to change your life in any way.
“The intelligent investor is a realist who sells to optimists and buys from pessimists.” | ― Benjamin Graham, The Intelligent Investor (75/25 - 50/50 - 25/75)
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