>Somewhere out there is a person who’s spent years running a 4 Sharpe ratio at her $5 million friends-and-family hedge fund, or her Robinhood personal account, but she never gets a job at a big hedge fund.
Weird numbers to pick here. I know like 10 guys off my personal contact list who can do 4 Sharpe at 5 million easy. The "game" in hedge funds isn't 4 Sharpe at 5mio AUM, its 1.5-2 Sharpe at 1b AUM or 1 Sharpe at 10b AUM, both of which are infinitely harder than 4 Sharpe at 5mio AUM. You can do 4 Sharpe at 5mio AUM after 6 years at a BB in anything that's not equities or delta 1.
dmoy 12 minutes ago [-]
> Weird numbers to pick here. I know like 10 guys off my personal contact list who can do 4 Sharpe at 5 million easy
Sure, but the pool of people who can get into hedge funds overlaps a ton with the pool of people who have done "6 years at a BB in anything that's not equities or delta". That's like... where hedge fund recruiters go poaching, isn't it?
I think the article was talking about random retail investors who can do this stuff, which seems relatively more rare.
em500 3 hours ago [-]
> Weird numbers to pick here. I know like 10 guys off my personal contact list who can do 4 Sharpe at 5 million easy. The "game" in hedge funds isn't 4 Sharpe at 5mio AUM, its 1.5-2 Sharpe at 1b AUM or 1 Sharpe at 10b AUM, b
So how do they do that? I'm a lot closer to 5 million than than 10b...
14 minutes ago [-]
ivape 6 minutes ago [-]
The WSB community most likely obliterates that metric, and I mean the broader community not the regards buying lotto tickets. You don’t need to look at Hedge Funds for good trading, you need to look at them for insider trading knowledge. IMHO that’s all they have on others because the only data that’s not available is that … inside stuff.
therobots927 3 hours ago [-]
These guys with 4.0 sharpe ratios at 5M AUM… are they running algos and if so at what time frame? I’m assuming building out the data / execution infra for that is expensive, not to mention the compute and storage power required to identify market inefficiencies after you have the infra built. You’re looking at a pretty significant upfront investment for that.
sjdfsjdfg93425 4 hours ago [-]
>You can do 4 Sharpe at 5mio AUM after 6 years at a BB in anything that's not equities or delta 1.
Can you explain for a non-finance audience?
mamonster 3 hours ago [-]
Sure, I'll give some numbers.
Sharpe ratio = (Your return annually - Annual Risk Free rate) / ( Annualized Vol of your portfolio).
BB = Bulge Bracket, basically a Tier 1 Bank (Goldman, UBS, MS, Citi, google the list).
Equities = Stocks.
Delta 1 = If underlying moves by X $, your product/ derivative moves by X $. Basically swaps, etfs, futures, etc.
Now for some numbers: Say you are under a "vanilla" 2/20 structure (which is actually like 10 years out of date but is still listed on all finance websites) where your fund charges a 2% management fee (i.e if you manage 5 mio USD you charge 100k per year for fund cost) and 20% performance rate on your gross above benchmark ( so you take 20% of the return above your benchmark).
Annualized SP500 vol is let's say 18%, your cash return right now is 3.5%. Quick maths gets you to 4 Sharpe is about 75% yearly return. ((75-3.5)/18 is about 4).Under these assumptions, 4 Sharpe return on 5 mio is 3.750mio.
Your performance fee as a HF manager is gonna be 0.715(75%-3.5%) x 0.2 x 5mio = 715k. So 4 Sharpe on 5mio is basically you earning 900k-1mio USD (depends on the jurisdiction for your base, i took like 180k USD for base) as the HF manager.
Edit: For people who don't trade professionally, capacity (i.e how much money your strategy/you as a trader accept before becoming inefficient/losing money) is the big filter. There's a shitload of strats that work at 1 mio USD but completely stop at 2mio or 5mio.
rokobobo 3 hours ago [-]
I think people were asking you to explain what kind of strategies people run at sharpe 4
mamonster 3 hours ago [-]
From people I know personally:
"Arbs" on stuff that big desks don't touch because of capacity (small mergers for example, you lever up on 2-3 small merger arbs per year and you are almost there);
DEX to liquidity pool latency arbs for shitcoins if you want a crypto example;
Edit: The other option is that if you are a trader in "special" markets (the best example is biotech/medstocks) where domain knowledge really matters being 4 sharpe is basically 1 good trade a year, and at 5mio USD AUM you are always at capacity.
bionsystem 2 hours ago [-]
I wonder why people always assume that the strategy would be algorithmic or systematic. How about global macro, long/short equity, or even plain long only done well ? Actually studying markets and assets fundamentally, and finding asymmetric bets ? There are plenty of people that have done that successfully over really long periods of time, I doubt markets are perfectly efficient just because some academics claim so, especially for bets with strong convexity.
jklein11 3 hours ago [-]
Equities and "delta 1 assets" are very liquid, meaning there are a lot of buyers and sellers. This helps to make price discover more efficient. Anything outside of that means that there is much less liquidity and therefore inefficiencies in price.
Think about it this way. You are trying to sell an apple. In one room, there are 100 people trying to sell an apples and 100 people trying to buy them. In the other room there is 1 person trying to buy apples and no one selling. In the first room you don't have much leverage. The buyers can go to the other 99 sellers if they don't like your price. In the second room you have a ton of leverage. If the person wants to buy an apple they are either going to have to buy it from you or wait for another seller to enter the room.
When it comes to non equity or delta 1 assets, there tends to be more complexity in understanding the assets, which acts as a barrier to entry. If you have been in investment banking for 6+ years, you likely understand these complexities and can find pricing inefficiencies.
missedthecue 3 hours ago [-]
Sharpe ratio is a metric that measures how much excess return an investment earns per unit of risk. So if someone says “this fund runs at a 4 Sharpe,” they mean the fund’s returns are four times the volatility, net of risk-free rate.
Super super ELI5 is that people don't like volatility in returns, even if the returns are good (i.e. down 40% one year, up 200% the next year is 34% CAGR, but crazy volatility). T-bills for example have extremely low volatility but also very low return. The holy grail is very low volatility with a great return. A 4 sharpe fund is in that quadrant.
You can also subscribe to Matt Levine as a newsletter and get it in your inbox Monday-Thursday. Sometimes it's quite hilarious.
fsckboy 4 hours ago [-]
I studied a lot of finance in grad school, at world leading elite finance school, and I am a very successful investor myself and can give you sound advice up and down the market and quibble your use of terminology.
(sad bear, or dog in lab with goggles meme)
I have no idea what a hedge fund is.
dinkblam 4 hours ago [-]
I studied a lot of computer science in grad school, at world leading elite CS school, and I am a very successful developer myself and can give you sound advice up and down the dev space and quibble your use of terminology.
…
I have no idea what a compiled language is.
fsckboy 4 hours ago [-]
i don't know what it means to not know what a compiled language is
skybrian 42 minutes ago [-]
I believe they are saying that computer languages can be implemented by compilers and by interpreters, so "compiled" is technically a property of the implementation, not the language.
But in casual use, "compiled language" means a language that is usually implemented using a compiler.
NoMoreNicksLeft 3 hours ago [-]
> I have no idea what a compiled language is.
This sounds like any of a dozen different computer science university programs I am familiar with.
jiggawatts 2 hours ago [-]
An interpreted language has a runtime that is essentially a function “i(script: string)” that immediately follows the instructions encoded in the string.
A compiler is a function “c(script: string) -> byte[]” that instead of running the script, outputs a binary that does the same thing as the interpreter, but more efficiently.
Commonly this means converting the human-readable script syntax to binary machine code that a CPU can run directly, but platforms like Java and .NET actually do this through multiple steps with an intermediate “byte code” that CPUs can’t execute without a lightweight runtime.
The benefit of the JIT is that it makes the compiler code portable to other CPU architectures without having to ship the source code. It is simple enough that interpreting it is just a “while” loop that bumps a pointer, reads the next instruction bytes, and uses a giant switch table to decide what to do.
If you squint at it, machine code is the same, except that the “loop and switch statement” is hard wired into the silicon.
SatvikBeri 4 hours ago [-]
There's no precise definition, but I prefer "funds that focus on alpha", as opposed to e.g. an index fund.
fsckboy 4 hours ago [-]
i'm not being snarky but, if you want to focus on alpha, construct a portfolio that removes beta, and nobody does that except portfolio theory.
so probably "funds that focus on obtaining private information, or flaws in public information"?
focusing on alpha and finding undiscovered alpha are not the same thing, and it's absolutely not clear and contrary to portfolio theory that you would succeed
2 hours ago [-]
wilkommen 4 hours ago [-]
Big is bad, actually. Centralization of power in a small number of hands creates structural market distortions, generates corruption, and diminishes the freedom of all.
loeg 4 hours ago [-]
Maybe read beyond the headline.
Herring 4 hours ago [-]
The article covers like 6 separate finance topics (news commentary). OP is right about the first one, eg expect highly restrictive non-competes and lower compensation over time.
xxpor 4 hours ago [-]
That's certainly one philosophical point of view, but it's not universally true.
My portfolio was +94% in 2024 and +52% in the past 6 months (I took a massive haircut thanks to April's tariff saga and by having biblical levels of greed...lesson learned).
How do I declare for the inaugural Hedge Fund Draft?
3 hours ago [-]
ivape 9 minutes ago [-]
Why would you want to work anywhere if you get returns like that every year?
3 hours ago [-]
Ekaros 4 hours ago [-]
So either they have to be big to play outside public markets. Or small enough that they can still exploit things... For actual hedge I might actually want to go for later. Especially if you look at premiums on say EA. And possibility of getting your money out in reasonable time.
themafia 4 hours ago [-]
> The point of a financial market is to allocate capital to its most productive uses. Someone who is very good at allocating capital should be allocating a lot of capital, not her own Robinhood account.
These two facts are not connected at all. There's no reason to assume the market cannot work or reliably find the "most productive" uses of capital in the aggregate.
> And an efficient market would allocate a lot of capital to her
Then that would give a single individual more control over the market than is healthy and would naturally tend towards inefficiency. The basic presumption here is that centralization of the economy around a limited number of entities is great for efficiency. I can find no examples in history of this and I can find many where this actually just increases corruption.
Given everything we learned about the "too big to fail" era I find articles like this to be obvious and grotesque lies.
gruez 4 hours ago [-]
>These two facts are not connected at all. There's no reason to assume the market cannot work or reliably find the "most productive" uses of capital in the aggregate.
Right, but just because it works "in the aggregate" doesn't mean that's how things work "should" work. I'm sure the road network would still muddle on if we allowed drunk drivers to drive, but we still ban them from driving. The article isn't even arguing for government intervention; it's just describing how things plays out naturally.
fsckboy 4 hours ago [-]
i had similar objections to yours but i would phrase the corrections differently.
>The point of a financial market is
no, the point of a financial market is to be a place where people who need money for lucrative projects can get it, and a place where people who have money can invest it, decoupling those transactions from the term of the investments and the irregularities of the different economic opportunities. To put it in simpler terms, think of the market of a town in medieval england, a financial market would allow you to know nothing in particular about farming but invest profitably in the farming activities of the town, getting what portion you want of your money back whenever you want it.
>to allocate capital to its most productive uses
is in the nature of a market that has the features markets need to function efficiently.
The point of a financial market is capital allocation, and people will partake even if the market is inefficient. Consider illegal/black markets, they are often cited as truly free markets where you can invest large sums of cash or buy anything for a price, and even though the prices are high, there are customers. Those markets can be made more efficient, but the fact they exist shows the power of markets without efficiency.
>>And an efficient market would allocate a lot of capital to her
>Then that would give a single individual more control over the market than is healthy
one of the features a market needs for efficiency (think of efficiency as "goods at a fair price") is that no participant alone can affect the prices; for that to be true there needs to be competition, and without it you get "market failure", a market where participants receive no benefit from participating. (markets should operate at a point where sellers are saying "that price offer is too low" and buyers are saying "that price offer is too high", but all the "great deal, I'll take it" transactions that already took place to get it to that point are were the happiness is created from thin air.) as new information emerges, prices can shift up and down to maintain that "take it or leave it" equilibrium.
no system is perfect, not democracy, not the courts, etc., but regulations and people mostly acting sensibly even in self interest makes markets the best method we have of allocating happiness most effectively.
being cynical about market capitalism is understandable, but it doesn't get you anywhere, other systems demand even more cynicism.
gruez 4 hours ago [-]
>no, the point of a financial market is to be a place where people who need money for lucrative projects can get it, and a place where people who have money can invest it
But all things being equal, investors would like their money allocated into projects with the best returns. Borrowers of course would prefer that they get the money so that doesn't really tell us anything, but society as a whole would rather that worthy projects are funded rather than a linear city in the desert or whatever.
>and people will partake even if the market is inefficient. Consider illegal/black markets, they are often cited as truly free markets where you can invest large sums of cash or buy anything for a price, and even though the prices are high, there are customers.
A good that can't be acquired on regular markets has a price of infinity. A black market might be more expensive than some place where it's legal, but it's still cheaper than the alternative.
fsckboy 3 hours ago [-]
>But all things being equal, investors would like their money allocated into projects with the best returns. Borrowers of course would prefer that they get the money so that doesn't really tell us anything, but society as a whole would rather that worthy projects are funded rather than a linear city in the desert or whatever.
you are describing the process by which competitive "jostling for the best returns / cheapest capital sources" produces market efficiency, which makes it pointless to try to find better returns or cheaper capital. Not having to think about that is a reward itself. The price of oil is established by auctioning off more oil every day; if you buy some at an auction, you're doing the best you can do, there is no better place to invest in oil, you can focus on driving your fleet of delivery trucks.
neilv 4 hours ago [-]
A bit off-topic to the post, but maybe very relevant to HN techbros seeing this article, and musing about becoming (lower caste) finance bros...
You know how there's a boots on the ground truth to what an early tech startup's Incentive Stock Options are actually worth nowadays, and how people should think about them (but that most startups won't admit)?
With that secret reality in mind, how should software engineer candidates considering working for a hedge fund or private equity job think about the compensation there? Maybe especially about "carry"?
A recruiter for a firm seeking a "Principal" level engineer, which would require moving to NYC, mentioned compensation of "$X salary, 50% bonus, and $Y carry". Where $X is a usual current non-FAANG Senior+ startup SWE salary, and Y is only a bit larger than X.
The recruiter opened by stating the single number $((X*1.5)+Y), as if it were the annual TC familiar to us from levels.fyi.
When I Google for "carry", it sounds like some speculative share of something unclear about some investments the firm owns or manages, and then this share might vest over 5-10 years, if I remain with the firm that long. The $Y dollar amount sounds like it's a fixed amount bonus or capped value of a share. Also unclear whether there's an additional $Y+ grant of carry each year.
If this were most tech startup ISOs, I would know that the ISOs were probably worth $0 or less, and in some ways rigged to be that way, even if the company has a successful exit from which people with real shares profit.
For this $((X*1.5)+Y) job, the $X salary alone will cover a lifestyle of renting a modest apartment in Brooklyn, plus decent savings building from whatever the rest of it is. I'm unclear whether the bonus and carry make it even competitive with Google L6, though.
What do I need to know about "carry" or other aspects of the compensation? What time horizons, conditions, and probabilities are involved?
alltheseas 4 hours ago [-]
[dead]
Rendered at 22:31:29 GMT+0000 (Coordinated Universal Time) with Vercel.
Weird numbers to pick here. I know like 10 guys off my personal contact list who can do 4 Sharpe at 5 million easy. The "game" in hedge funds isn't 4 Sharpe at 5mio AUM, its 1.5-2 Sharpe at 1b AUM or 1 Sharpe at 10b AUM, both of which are infinitely harder than 4 Sharpe at 5mio AUM. You can do 4 Sharpe at 5mio AUM after 6 years at a BB in anything that's not equities or delta 1.
Sure, but the pool of people who can get into hedge funds overlaps a ton with the pool of people who have done "6 years at a BB in anything that's not equities or delta". That's like... where hedge fund recruiters go poaching, isn't it?
I think the article was talking about random retail investors who can do this stuff, which seems relatively more rare.
So how do they do that? I'm a lot closer to 5 million than than 10b...
Can you explain for a non-finance audience?
Sharpe ratio = (Your return annually - Annual Risk Free rate) / ( Annualized Vol of your portfolio).
BB = Bulge Bracket, basically a Tier 1 Bank (Goldman, UBS, MS, Citi, google the list).
Equities = Stocks.
Delta 1 = If underlying moves by X $, your product/ derivative moves by X $. Basically swaps, etfs, futures, etc.
Now for some numbers: Say you are under a "vanilla" 2/20 structure (which is actually like 10 years out of date but is still listed on all finance websites) where your fund charges a 2% management fee (i.e if you manage 5 mio USD you charge 100k per year for fund cost) and 20% performance rate on your gross above benchmark ( so you take 20% of the return above your benchmark).
Annualized SP500 vol is let's say 18%, your cash return right now is 3.5%. Quick maths gets you to 4 Sharpe is about 75% yearly return. ((75-3.5)/18 is about 4).Under these assumptions, 4 Sharpe return on 5 mio is 3.750mio.
Your performance fee as a HF manager is gonna be 0.715(75%-3.5%) x 0.2 x 5mio = 715k. So 4 Sharpe on 5mio is basically you earning 900k-1mio USD (depends on the jurisdiction for your base, i took like 180k USD for base) as the HF manager.
Edit: For people who don't trade professionally, capacity (i.e how much money your strategy/you as a trader accept before becoming inefficient/losing money) is the big filter. There's a shitload of strats that work at 1 mio USD but completely stop at 2mio or 5mio.
"Arbs" on stuff that big desks don't touch because of capacity (small mergers for example, you lever up on 2-3 small merger arbs per year and you are almost there);
DEX to liquidity pool latency arbs for shitcoins if you want a crypto example;
Pure arbs (One of my friends who admittedly is not satisfied with 1mio USD comp did this trade: https://notion.moontowermeta.com/financial-hacking-etf-vs-ne... ).
Edit: The other option is that if you are a trader in "special" markets (the best example is biotech/medstocks) where domain knowledge really matters being 4 sharpe is basically 1 good trade a year, and at 5mio USD AUM you are always at capacity.
Think about it this way. You are trying to sell an apple. In one room, there are 100 people trying to sell an apples and 100 people trying to buy them. In the other room there is 1 person trying to buy apples and no one selling. In the first room you don't have much leverage. The buyers can go to the other 99 sellers if they don't like your price. In the second room you have a ton of leverage. If the person wants to buy an apple they are either going to have to buy it from you or wait for another seller to enter the room.
When it comes to non equity or delta 1 assets, there tends to be more complexity in understanding the assets, which acts as a barrier to entry. If you have been in investment banking for 6+ years, you likely understand these complexities and can find pricing inefficiencies.
Super super ELI5 is that people don't like volatility in returns, even if the returns are good (i.e. down 40% one year, up 200% the next year is 34% CAGR, but crazy volatility). T-bills for example have extremely low volatility but also very low return. The holy grail is very low volatility with a great return. A 4 sharpe fund is in that quadrant.
(sad bear, or dog in lab with goggles meme)
I have no idea what a hedge fund is.
…
I have no idea what a compiled language is.
But in casual use, "compiled language" means a language that is usually implemented using a compiler.
This sounds like any of a dozen different computer science university programs I am familiar with.
A compiler is a function “c(script: string) -> byte[]” that instead of running the script, outputs a binary that does the same thing as the interpreter, but more efficiently.
Commonly this means converting the human-readable script syntax to binary machine code that a CPU can run directly, but platforms like Java and .NET actually do this through multiple steps with an intermediate “byte code” that CPUs can’t execute without a lightweight runtime.
The benefit of the JIT is that it makes the compiler code portable to other CPU architectures without having to ship the source code. It is simple enough that interpreting it is just a “while” loop that bumps a pointer, reads the next instruction bytes, and uses a giant switch table to decide what to do.
If you squint at it, machine code is the same, except that the “loop and switch statement” is hard wired into the silicon.
so probably "funds that focus on obtaining private information, or flaws in public information"?
focusing on alpha and finding undiscovered alpha are not the same thing, and it's absolutely not clear and contrary to portfolio theory that you would succeed
https://www.theargumentmag.com/p/the-problem-with-bossbabe-l...
How do I declare for the inaugural Hedge Fund Draft?
These two facts are not connected at all. There's no reason to assume the market cannot work or reliably find the "most productive" uses of capital in the aggregate.
> And an efficient market would allocate a lot of capital to her
Then that would give a single individual more control over the market than is healthy and would naturally tend towards inefficiency. The basic presumption here is that centralization of the economy around a limited number of entities is great for efficiency. I can find no examples in history of this and I can find many where this actually just increases corruption.
Given everything we learned about the "too big to fail" era I find articles like this to be obvious and grotesque lies.
Right, but just because it works "in the aggregate" doesn't mean that's how things work "should" work. I'm sure the road network would still muddle on if we allowed drunk drivers to drive, but we still ban them from driving. The article isn't even arguing for government intervention; it's just describing how things plays out naturally.
>The point of a financial market is
no, the point of a financial market is to be a place where people who need money for lucrative projects can get it, and a place where people who have money can invest it, decoupling those transactions from the term of the investments and the irregularities of the different economic opportunities. To put it in simpler terms, think of the market of a town in medieval england, a financial market would allow you to know nothing in particular about farming but invest profitably in the farming activities of the town, getting what portion you want of your money back whenever you want it.
>to allocate capital to its most productive uses
is in the nature of a market that has the features markets need to function efficiently.
The point of a financial market is capital allocation, and people will partake even if the market is inefficient. Consider illegal/black markets, they are often cited as truly free markets where you can invest large sums of cash or buy anything for a price, and even though the prices are high, there are customers. Those markets can be made more efficient, but the fact they exist shows the power of markets without efficiency.
>>And an efficient market would allocate a lot of capital to her
>Then that would give a single individual more control over the market than is healthy
one of the features a market needs for efficiency (think of efficiency as "goods at a fair price") is that no participant alone can affect the prices; for that to be true there needs to be competition, and without it you get "market failure", a market where participants receive no benefit from participating. (markets should operate at a point where sellers are saying "that price offer is too low" and buyers are saying "that price offer is too high", but all the "great deal, I'll take it" transactions that already took place to get it to that point are were the happiness is created from thin air.) as new information emerges, prices can shift up and down to maintain that "take it or leave it" equilibrium.
no system is perfect, not democracy, not the courts, etc., but regulations and people mostly acting sensibly even in self interest makes markets the best method we have of allocating happiness most effectively.
being cynical about market capitalism is understandable, but it doesn't get you anywhere, other systems demand even more cynicism.
But all things being equal, investors would like their money allocated into projects with the best returns. Borrowers of course would prefer that they get the money so that doesn't really tell us anything, but society as a whole would rather that worthy projects are funded rather than a linear city in the desert or whatever.
>and people will partake even if the market is inefficient. Consider illegal/black markets, they are often cited as truly free markets where you can invest large sums of cash or buy anything for a price, and even though the prices are high, there are customers.
A good that can't be acquired on regular markets has a price of infinity. A black market might be more expensive than some place where it's legal, but it's still cheaper than the alternative.
you are describing the process by which competitive "jostling for the best returns / cheapest capital sources" produces market efficiency, which makes it pointless to try to find better returns or cheaper capital. Not having to think about that is a reward itself. The price of oil is established by auctioning off more oil every day; if you buy some at an auction, you're doing the best you can do, there is no better place to invest in oil, you can focus on driving your fleet of delivery trucks.
You know how there's a boots on the ground truth to what an early tech startup's Incentive Stock Options are actually worth nowadays, and how people should think about them (but that most startups won't admit)?
With that secret reality in mind, how should software engineer candidates considering working for a hedge fund or private equity job think about the compensation there? Maybe especially about "carry"?
A recruiter for a firm seeking a "Principal" level engineer, which would require moving to NYC, mentioned compensation of "$X salary, 50% bonus, and $Y carry". Where $X is a usual current non-FAANG Senior+ startup SWE salary, and Y is only a bit larger than X.
The recruiter opened by stating the single number $((X*1.5)+Y), as if it were the annual TC familiar to us from levels.fyi.
When I Google for "carry", it sounds like some speculative share of something unclear about some investments the firm owns or manages, and then this share might vest over 5-10 years, if I remain with the firm that long. The $Y dollar amount sounds like it's a fixed amount bonus or capped value of a share. Also unclear whether there's an additional $Y+ grant of carry each year.
If this were most tech startup ISOs, I would know that the ISOs were probably worth $0 or less, and in some ways rigged to be that way, even if the company has a successful exit from which people with real shares profit.
For this $((X*1.5)+Y) job, the $X salary alone will cover a lifestyle of renting a modest apartment in Brooklyn, plus decent savings building from whatever the rest of it is. I'm unclear whether the bonus and carry make it even competitive with Google L6, though.
What do I need to know about "carry" or other aspects of the compensation? What time horizons, conditions, and probabilities are involved?