Why investing SS in the stock market is a horrible idea.

[Boss]

Great post, Toro! Well said!

 

[FA_Q2]

They idea that you cant invest your own money is ludicrous.

But then so is the lie that SS is our own money. It's a ponzi scheme. Our money is going to people who are already collecting.

SS allows the rich to steal from the poor.

Let me explain to you how the American Government works. Let's go back to Reagan.

First you lower taxes on the wealthy. Then you raise taxes on wage earners, telling them the money will be held in trust for Social Security. Then you raid the trust in order to hand out subsidies to corporations and pay for things like Star Wars. Then, 50 years later, you tell the poor that they will have to take a haircut on benefits.

But it gets better. It's important that the poor don't realize how bad you are fucking them. So you set-up radio and TV stations that bitch 24/7 about welfare payouts to the lazy, but you never mention who government really serves. Instead, you use your considerable media assets to redirect the understandable rage of the poor away from the concentrated wealth that owns government.

Mostly true minus the rhetoric and hate but that really is the point as to why SS would be so much better invested rather than squandered. It would give the poor REAL assets. There would be no ‘haircut’ and such assets can be passed on.

You do realize that you just made a good case for PRIVATIZING SS, right?

 

[FA_Q2]

But that is what pay as you go plan is by definition. There is no real fund. If you want to pay (interest) to the fund you need to tax it from the people - exactly the same if there wasn't any fund at all. Thus saying that something was robbed is kind of wrong.

Also pay as you go plan doesn't necessarily require an ever growing economy and population. The plan hurts people whether the economy grows or not. It just less noticable if there are more people and greater economy to pay for it. The interest is STILL effectevely lost though, it's just easier to pay for it if the population has grown.

That’s incorrect. With a decreasing working population, there is NOT enough money coming in to cover the expenses going out. That is a cold hard fact and no way around that. This is why a growing population is REQUIRED. Obviously, you are going to draw more in a yare than you are going to pay as such you require more than a single worker paying into the system than drawing from that system. The close that number gets to a 1:1 ratio, the worse the problem gets, hence you need more going into the system than you have exiting it in order for it to be sustainable.

We had seen this coming; that is why the SS taxes were DOUBLED. Of course, we spent that too so there really was zero gain in that debacle.

What I meant is that if you have, for example a population of 100.000 who earn 100K a year and a other population of 50.000 who earn 10K a year, obviously it's easier to pay 10 million in retirement benefits for the first population.

The loss of 10 million is just as real either way though. And in a case where the population doesn't grow you would massively have to increase taxes. But in BOTH CASES you have lost 10 million. The "failure" is there either way, it's just easier to pay for it with increasing population and improving economy. Just like it is for anything. That 10 million could have been used to do other things if not for the SS. The benefits of growing economy and population are partially lost.



Now, if the population invested into stocks and equities overseas, the interest would actually be real and not just taxed back from the population. There would be no 10 million hole, there would be perhaps 1 million gained in interest instead, no one would have to be taxed. And it would not matter if the population shrank like a shark. That would be a real invstment plan.

That makes some sense. My point was though that if you have a decreasing pool of people to draw from it becomes untenable to pay them at some point. Sure, the loss is the same no matter what but the real impact grows to the point where it can no longer be floated.

As you said, if we went to an investment instead, that would not mean anything. Should the population decrease, so what. Those assets would be real and would not dry up simply because others were not paying into the system. Of course the real benefit is in the fact that you get back what you put in, even if you die young.

 

[Norman]

That’s incorrect. With a decreasing working population, there is NOT enough money coming in to cover the expenses going out. That is a cold hard fact and no way around that. This is why a growing population is REQUIRED. Obviously, you are going to draw more in a yare than you are going to pay as such you require more than a single worker paying into the system than drawing from that system. The close that number gets to a 1:1 ratio, the worse the problem gets, hence you need more going into the system than you have exiting it in order for it to be sustainable.

We had seen this coming; that is why the SS taxes were DOUBLED. Of course, we spent that too so there really was zero gain in that debacle.

What I meant is that if you have, for example a population of 100.000 who earn 100K a year and a other population of 50.000 who earn 10K a year, obviously it's easier to pay 10 million in retirement benefits for the first population.

The loss of 10 million is just as real either way though. And in a case where the population doesn't grow you would massively have to increase taxes. But in BOTH CASES you have lost 10 million. The "failure" is there either way, it's just easier to pay for it with increasing population and improving economy. Just like it is for anything. That 10 million could have been used to do other things if not for the SS. The benefits of growing economy and population are partially lost.



Now, if the population invested into stocks and equities overseas, the interest would actually be real and not just taxed back from the population. There would be no 10 million hole, there would be perhaps 1 million gained in interest instead, no one would have to be taxed. And it would not matter if the population shrank like a shark. That would be a real invstment plan.

That makes some sense. My point was though that if you have a decreasing pool of people to draw from it becomes untenable to pay them at some point. Sure, the loss is the same no matter what but the real impact grows to the point where it can no longer be floated.

As you said, if we went to an investment instead, that would not mean anything. Should the population decrease, so what. Those assets would be real and would not dry up simply because others were not paying into the system. Of course the real benefit is in the fact that you get back what you put in, even if you die young.

Yeah, some people like the fact that you can get the money back even if you die young. Some however don't and would rather enjoy the security in the case that you live very long.

Bad news is, the government gives you no choice and you are forced into a form of defined benefit plan. This is really unnecessary even IF you use pay as you go system. But it's what it is.

In free markets both plans are provided. You can choose whether you want defined contribution plan or defined benefit plan.

I would rather have a private system where the government provided a very small retirement just enough to live by and the rest would be up to you (or perhaps you would be forced to invest some of your earnings). But the problem is, it's very hard to go from pay as you go to any other scheme as where is the money come from to pay the existing retirees?

Even the swedish system is much better, in it the retirement benefits basically scale according to the economy. Although, it's difficult to point out to a system that is worse than the SS so no surprise there. In most countries at least some amount of the money was intially invested, not so in USA. Every penny was spent on star wars and other... for sure profit generating ventures. And then people were left with an impression that they actually paid into some fund, which just makes it that much worse. Even today many people seem to believe that there is some sort of fund. I guess they don't' know what "Pay as you go" means.

The irony is, to my knowledge SS was originally created partly because the fact that it was feared a lot of people would not save money and thus would be a burden on the society when they retire.... So the government decided to then spend everybody's retirement money and now every single retiree is a burden to the tax payer.



EDIT: And yes I completely understand where you are coming from, in my previous post I just wanted to explain the losses are there whether the economy grows or not. It's in fact impossible to run a ponzi scheme indefinitely without the investor base growing, that is correct. And in that sense payasyougo scheme must straight out crash if any real interest is promised in a static economy. For example the first generations retirement payment is 1000, with 20% interest. Now the second generation must pay 1200 to pay the retirees benefits with interest... the third generation must again pay 20% more and so on. At some point the whole GDP is going to be retirement payments.

 

[FA_Q2]

Yeah, some people like the fact that you can get the money back even if you die young. Some however don't and would rather enjoy the security in the case that you live very long.

Bad news is, the government gives you no choice and you are forced into a form of defined benefit plan. This is really unnecessary even IF you use pay as you go system. But it's what it is.

In free markets both plans are provided. You can choose whether you want defined contribution plan or defined benefit plan.

I see no reason that the government could not offer the same dual system either. If these people really want SS as it stands, then they could pay into some sort of insurance plan as well then. My beef, and it seems yours as well, is the government has forced us all into an asinine system that has essentially zero benefits over a balanced retirement plan. That is what happens in our government though.

I would rather have a private system where the government provided a very small retirement just enough to live by and the rest would be up to you (or perhaps you would be forced to invest some of your earnings). But the problem is, it's very hard to go from pay as you go to any other scheme as where is the money come from to pay the existing retirees?

VERY true. That is one of the fundamental problems that we are running into – swapping over is going to be VERY expensive. Of course, the longer we wait, the worse that swap gets. Not a good reason to continue on.

Anything this large and on this type of monetary scale needs to be phased in over a long period of time.

Even the swedish system is much better, in it the retirement benefits basically scale according to the economy. Although, it's difficult to point out to a system that is worse than the SS so no surprise there. In most countries at least some amount of the money was intially invested, not so in USA. Every penny was spent on star wars and other... for sure profit generating ventures. And then people were left with an impression that they actually paid into some fund, which just makes it that much worse. Even today many people seem to believe that there is some sort of fund. I guess they don't' know what "Pay as you go" means.

The government itself perpetuated this asinine concept in talking constantly about the SS ‘trust fund’ that supposedly is 2 trillion strong. In that same breath, the left demands that SS does not add one red cent onto the deficit. Never mind that they are using interest paid by the general fund right now to cover their expenses.

The really sad part of this, to me, is that the original program was, for all intents and purposes, a sham. Average life expectancy in 1935, when SS started, was 61 years old. Essentially, many people did not even live long enough to get SS in the first place even though they paid into it. SS attempt to deny this BUT even using their figures that remove mortality rates below 21 for the ‘adult’ average lifespan and you still end up with just over half (57%) of people that lived long enough to even collect social security. The rest, of course, gained nothing.

The irony is, to my knowledge SS was originally created partly because the fact that it was feared a lot of people would not save money and thus would be a burden on the society when they retire.... So the government decided to then spend everybody's retirement money and now every single retiree is a burden to the tax payer.

LOL. Good point and spot on.

 

[Boss]

The irony is, to my knowledge SS was originally created partly because the fact that it was feared a lot of people would not save money and thus would be a burden on the society when they retire....

It wasn't feared, it was a very real problem. Old people were quite literally starving in the streets, homeless and destitute. Of course, this was in the midst of the Great Depression, where people lost any 'savings' they might have socked away. The initial idea was noble, and it's still a well-intentioned idea. The problem has been, keeping Congressional hands off the money. In 1969, legislation that was passed under LBJ came into effect, which gave us a "unified budget" ...combining the SS trust fund and other general revenues. This accounting gimmick made it appear we had a surplus, so Congress immediately began to think of ways to spend it. That wasn't hard to do, and by 1996, the trust fund was essentially full of IOUs. The only reason the SS became so big, was the Baby Boomer generation, which dwarfed previous working generations. Now that they are retiring, the money is gone. We don't have enough workers to pay their retirements, and the trust fund is full of IOUs.

Now we can argue all day long about who's fault that is, or who voted for what and when, it doesn't help solve the problem or address the future. I think there are several things we need to do, in order to revamp the system, and ensure that future generations have a security system that works under any circumstance. This means partial privatization. That word seems to frighten liberals for some reason, they envision bumbling dolts who wouldn't invest wisely, becoming a burden on society. But it's a really simple concept to transition to, and can be done without the risk of this happening.

First of all, people who have attained a certain amount of wealth in their lifetime, enough to securely care for themselves in old age, should be able to opt out entirely. They would only contribute to SS until they've reached that level, and they wouldn't receive benefits. A "basic" contribution could be made to a general SS trust fund, which would pay a small benefit upon retirement, much like what we currently have. However, there would be the optional IRA-type investment, which we make mandatory by law, just as SSI is now mandatory by law. You have to contribute to your own account, if you work. So it's like a forced savings account, but it is your asset and your property when you reach retirement. If you don't make it to retirement, your spouse and children can collect the amount you paid in, through a monthly disbursement, for as long as they live or until the funds are depleted, at which time, they would revert to the old 'basic' system. You would never be able to withdraw the money in a lump sum, although a provision could be made to withdraw larger amounts in hardship cases or special circumstances. If this had been the original setup, current retirees would have bank accounts with $800k at least, plenty of money to live the rest of their lives comfortably, and still leave their families something. As it stands, we're approaching a time when retirees will have nothing, because the government is broke and can't pay the monthly benefits.

 

[LogikAndReazon]

Social Security in a guranteed , menial return, fixed, civil servant managed account is perfect for handicapped folks like this poster........

 

[OohPooPahDoo]

So somehow the bond is able to generate interest without anyone paying that said interest?

Is that what I said? No, its not. What I said was: "If you want more interest than you pay in taxes - buy bonds." Do you need me to explain the meaning of that English sentence to you?



Social Security is pay as you go. Have you been paying attention?

Problem is you are pretending that social security is some sort of investment plan that makes great returns.

I'm not. Social Security is an insurance product, not an investment product - and it should remain that way. You could buy the almost same thing in the private market by packaging a disability insurance plan with a life annuity.

Annuities are paid out of pools of capital that invest in other assets besides government bonds.

Insurance companies invest capital in the stock market.

Annuities are guaranteed by the insurance company regardless of the performance of any assets they have purchased with the funds.

 

[OohPooPahDoo]

It argues, it's a bad idea to keep our money and invest in a stock market

No it doesn't. It argues that social security funds being invested in the stock market is a bad idea. Outside of that I'd encourage you to buy as much stock as you can - it will make my portfolio more valuable.

Hey dimwit, where do you think social security funds come from? It's OUR money! I'm happy that you realize and understand, if I invest MY money, it helps you. Now, if I could actually GET my money so I can invest it, everything will be just fine!

The problem is, you're a brainwashed little tool for the left, who doesn't want to relinquish power and control of MY money. It helps to fund too many of your idiotic knee-jerk whims.

The Social Security taxes you have paid have been spent on retirement benefits for the currently retired. I suppose you feel that we should just screw over old people and let you keep your money.

 

[OohPooPahDoo]

I said way back that a basic tenet of economic theory is that there is a trade-off between risk and reward. Every student in finance 101 is taught this. Risk neutrality does not change this. Risk neutrality does not mean that investors don't want to take any risk, nor that they don't want to be compensated for taking risk. It says that prices must be adjusted for risk preferences.

No, it doesn't mean that. Risk neutral investors do not adjust price with risk. That's the very definition of risk neutral.

"Risk aversion" does not mean people don't want to take on any risk. It means that they over-estimate risk, and need to be paid more to take it on. It means people will take a lower return for a more certain outcome than a higher return with a less certain outcome, even if the expected probabilities are the same.

Yes, that is true. Unfortunately any attempt to price options contracts with an assumption of risk averse investing fails miserably.

Modern portfolio theory states that there is a trade-off between risk and return. In MPT, the higher the risk, the higher return.

Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return

Those two statements aren't the same thing. In one you say that higher return means higher risk, and in the other you say there is a way you can get around the higher risk while keeping the high return.

EDIT - To clarify, economic theory states that an investor must be compensated to take on more risk.

WHAT economic theory? Are you aware there are multitudes of economic theories all describing the same things and often failing miserably? On the other hand, the black scholes pricing model has proven exceptionally accurate for a finance theory, and it presumes - in fact requires - risk neutrality.

If it is indeed true that over 30 year periods the market will always beat treasuries, there would be young arbitragers lining up to leverage as much capital as possible to buy as much of the stock market as humanly possible - guaranteeing themselves pay out in 30 years. If you're so certain you're right, why not borrow on the stocks you have now and leverage your account as much as you can? Why not buy call options on stocks and indexes instead of the underlying?

 

[Boss]

No it doesn't. It argues that social security funds being invested in the stock market is a bad idea. Outside of that I'd encourage you to buy as much stock as you can - it will make my portfolio more valuable.

Hey dimwit, where do you think social security funds come from? It's OUR money! I'm happy that you realize and understand, if I invest MY money, it helps you. Now, if I could actually GET my money so I can invest it, everything will be just fine!

The problem is, you're a brainwashed little tool for the left, who doesn't want to relinquish power and control of MY money. It helps to fund too many of your idiotic knee-jerk whims.

The Social Security taxes you have paid have been spent on retirement benefits for the currently retired. I suppose you feel that we should just screw over old people and let you keep your money.

No, I think you should pay them back their money, that you borrowed and spent, on your frivolous little social entitlement programs and whatnot, by cutting those programs, and let me keep my money so this doesn't happen again in the future.

 

[OohPooPahDoo]

Hey dimwit, where do you think social security funds come from? It's OUR money! I'm happy that you realize and understand, if I invest MY money, it helps you. Now, if I could actually GET my money so I can invest it, everything will be just fine!

The problem is, you're a brainwashed little tool for the left, who doesn't want to relinquish power and control of MY money. It helps to fund too many of your idiotic knee-jerk whims.

The Social Security taxes you have paid have been spent on retirement benefits for the currently retired. I suppose you feel that we should just screw over old people and let you keep your money.

No, I think you should pay them back their money, that you borrowed and spent, on your frivolous little social entitlement programs and whatnot, by cutting those programs, and let me keep my money so this doesn't happen again in the future.

I didn't borrow any money from retirees.

You're the on complaining that they get their benefits paid, not me.

 

[Toro]

Economic theory says that higher risk should be compensated with higher rewards. A rational investor needs to be compensated for taking on more risk. This assumption is what the entire theory of modern finance is based upon. If you think that is wrong, then you better alert every single university in the world because that's what they are teaching their students.

But do not mistake that I'm saying every single individual should always be invested in the stock market. It depends on each individual's risk preference. And it depends on valuation and time frames. At times over the past 15 years, I've been short. Right now, I'm about 75% invested in my personal account, mostly highly concentrated in one industry that I think is dirt cheap. I have been as much as 220% long, which I was in gold in 2009. I tried to short Tnotes last year and buy high dividend paying stocks but my brokers had no inventory to lend. So I just bought the stocks in smaller size.

If someone offered me a 30-year swap of the S&P 500 against 30-year Treasury bond, I'd do that right now.

 

[OohPooPahDoo]

Economic theory says that higher risk should be compensated with higher rewards. A rational investor needs to be compensated for taking on more risk. This assumption is what the entire theory of modern finance is based upon.

If there were risk-aversion in the options market, it would have to be balanced by risk seeking behaviour on the other side of the transaction. Take for instance, a binary call option with a 10 to 1 chance expiring in the money and paying out $10. The risk-averse investor would not pay $1 for this option, he would want pay less than $1. The trouble is - he has to find someone to sell it to him - and the other side of that transaction would have to be risk seeking! If you demand to pay only $0.75 for an option with a 1 in 10 chance of having to pay you $10 - who would sell you that contract? Only someone willing to take LESS money for the same risk - a risk-seeker. But no competent derivatives dealer would sell a binary with a 10 to 1 chance at a payout for anything less than $1.00 before the bid/ask spread and commissions! So the risk-averse investor doesn't even get to play in the options market because no one will sell to or buy options from him at the price he desires. The CBOE may as well put up a sign that says "risk neutral investors only" - because any risk-averse investors will not find the price they want and any risk-seeking investors will simply be gobbled up by the arbitrageurs (some within seconds).


EDIT: Perhaps the equity premium in the stock market is possible because the risk-aversion of investors is balanced by risk-seeking on the side of companies that offer public stock. When the owners of a company decide to offer part of it to the public, they are essentially making a bet that the value of the cash raised in the offering (and what they can do with the cash) is worth more to them than the liabilities incurred by having to now give up whatever % of their profits they have to pay to the public share float. However - if they are risk-seeking, they will be willing to take less cash for the shares. Risk-seeking behavior can occur when its all-or-nothing. For instance, if you owe $1000 on your house note and if you don't pay it tomorrow you will lose your home, you might be willing to pay $200 for a 10 to 1 bet to win $1000 because the $200 won't save your home. A new company can be in an all-or-nothing position - where they have to raise lots of cash through selling shares, or they will not be able to continue growing and risk being over-run by their competitors who are better financed. So they will be willing to discount those shares.

I submit that the equity premium may be a result of risk-seeking behaviour by the sale of stock by the underlying corporations (either in the IPO or subsequent offerings)


Its worth thinking about these things and doing a little research into risk-neutrality and arbitrage free pricing before mindlessly repeating again "economic theory says...."

 

[flacaltenn]

No it doesn't. It argues that social security funds being invested in the stock market is a bad idea. Outside of that I'd encourage you to buy as much stock as you can - it will make my portfolio more valuable.

Hey dimwit, where do you think social security funds come from? It's OUR money! I'm happy that you realize and understand, if I invest MY money, it helps you. Now, if I could actually GET my money so I can invest it, everything will be just fine!

The problem is, you're a brainwashed little tool for the left, who doesn't want to relinquish power and control of MY money. It helps to fund too many of your idiotic knee-jerk whims.

The Social Security taxes you have paid have been spent on retirement benefits for the currently retired. I suppose you feel that we should just screw over old people and let you keep your money.

Of course -- when we WERE running $80Bill /year in surplus --- WE COULD have used that money to defer FUTURE payments, by letting some folks partially opt out.. If you're forced into a negative ROI --- doesn't matter if it's 20% or 25%.... So I would have volunteered to have future benefits cut by an amount greater than the exemption I was getting..

OR --- why shouldn't the "premiums" include a 2% kicker ABOVE expected payment liabilities to build up a REAL investment fund? 2% would move the SS FICA from about 12.2% to 12.5%. Trivial amount per paycheck.. Brings in a 4 or 5 $BILL/yr to invest..

That's how real people invest for their future..

 

[Toro]

Economic theory says that higher risk should be compensated with higher rewards. A rational investor needs to be compensated for taking on more risk. This assumption is what the entire theory of modern finance is based upon.

If there were risk-aversion in the options market, it would have to be balanced by risk seeking behaviour on the other side of the transaction. Take for instance, a binary call option with a 10 to 1 chance expiring in the money and paying out $10. The risk-averse investor would not pay $1 for this option, he would want pay less than $1. The trouble is - he has to find someone to sell it to him - and the other side of that transaction would have to be risk seeking! If you demand to pay only $0.75 for an option with a 1 in 10 chance of having to pay you $10 - who would sell you that contract? Only someone willing to take LESS money for the same risk - a risk-seeker. But no competent derivatives dealer would sell a binary with a 10 to 1 chance at a payout for anything less than $1.00 before the bid/ask spread and commissions! So the risk-averse investor doesn't even get to play in the options market because no one will sell to or buy options from him at the price he desires. The CBOE may as well put up a sign that says "risk neutral investors only" - because any risk-averse investors will not find the price they want and any risk-seeking investors will simply be gobbled up by the arbitrageurs (some within seconds).

There are arbitrageurs who take advantage of that. The implied volatility of options is generally higher than realized volatility. The arbitrageurs write options and collect the premium, then hedge the underlying.

There is a great deal of empirical evidence that people consistently over-estimate downside risk. This behavior is all over the financial markets.

 

[Toro]

Its worth thinking about these things and doing a little research into risk-neutrality and arbitrage free pricing before mindlessly repeating again "economic theory says...."

Like I said, take it up with every university in the world that teaches finance and economics because that is what they teach.

 

[Boss]

The Social Security taxes you have paid have been spent on retirement benefits for the currently retired. I suppose you feel that we should just screw over old people and let you keep your money.

No, I think you should pay them back their money, that you borrowed and spent, on your frivolous little social entitlement programs and whatnot, by cutting those programs, and let me keep my money so this doesn't happen again in the future.

I didn't borrow any money from retirees.

You're the on complaining that they get their benefits paid, not me.

Yes, your political representatives that you voted for and supported, were acting on your behalf at your request, to pilfer their money and spend it on entitlement. Now the money is gone, and you think it should be MY responsibility to pay it back?

I am NOT complaining they get their benefits paid, they SHOULD have their benefits paid, they put their money it it all their lives. You spent their money, now you need to repay what you borrowed from them. In order to do this, we need to eliminate all the entitlement programs you borrowed the money to fund, the earmarks you authorized for the sake of votes to your favorite representatives, and the interest you owe on your debt to them. Then we need to abolish the system which allowed you to get your grubby little hands on OUR money, and install a system which guarantees that can never happen again.

 

[Toro]

I said way back that a basic tenet of economic theory is that there is a trade-off between risk and reward. Every student in finance 101 is taught this. Risk neutrality does not change this. Risk neutrality does not mean that investors don't want to take any risk, nor that they don't want to be compensated for taking risk. It says that prices must be adjusted for risk preferences.

No, it doesn't mean that. Risk neutral investors do not adjust price with risk. That's the very definition of risk neutral.

Yes it does. My mistake.

Risk neutrality is used in options theory to price options. It's an assumption to make options pricing mathematically easier. It doesn't mean that all financial markets are risk neutral. It assumes that the expected return on stocks is the risk-free rate. Modern portfolio theory says otherwise.

 

[Toro]

So I decided to revisit risk neutrality. Here is what it says in Introduction to Futures and Options Markets, Second Edition, by John C Hull, page 270.

Note that risk-neutral valuation does not state that investors are risk neutral. What it does state is that derivative securities such as options can be valued on the assumption that investors are risk neutral.

IOW, risk neutrality is used to price options, not to make a general statements about the behavior of financial market participants.

EDIT - Also, from page 245

The expected return on all stocks in a risk-neutral world is the risk-free rate.

Clearly, MPT says otherwise, as demonstrated in CAPM where stocks are a function of volatility and the expected return of the market above the risk-free rate.