The Hidden Math of Winning in Trading

Mulham Trading explains 30 hidden math lessons for traders: why losses hurt more than gains, how streaks and swings erode accounts, and why position sizing and edge matter.

Key Takeaways

Protect capital first, because losses compound against you more harshly than gains compound for you.
Judge a strategy by drawdowns, streak tolerance, and risk per trade, not just average return or win rate.
Keep per-trade risk small (around 1%) and account for correlation across open positions.
Recognize that short-term results are dominated by randomness; a small edge needs hundreds or thousands of trades to confirm.

What the video covers

Losses are harder to recover from than gains: a 50% loss needs a 100% gain to break even, and the required recovery grows steeper as losses deepen.
Equal percentage wins and losses still shrink an account because each loss is taken from a larger balance than the following gain.
A high average return can hide large swings; volatile strategies with the same average can end far lower than smooth ones.
A coin-flip game with positive average returns still left about 76% of players with losses, showing that averages can mislead about individual outcomes.
Even strategies with a good win rate produce long losing streaks, which are normal statistical behavior rather than proof the strategy broke.
Most trades in simulations occur while the account is below its prior peak, meaning recovery often takes many trades.
Position size must account for both dollar risk and stop distance, and risk per trade strongly determines drawdown depth.
Correlated positions behave like one larger bet, so several 'diversified' trades can lose together.
Real markets have fatter tails than a bell curve, so extreme moves happen more often than simple models predict.
Small edges require very large sample sizes before they can be distinguished from luck, so traders must survive long enough to measure them.

Chapters

Why does a 50% loss require a 100% gain to recover?

Because the gain is applied to a smaller remaining balance. After losing 50% of $100, you have $50, so you need to double it, a 100% gain, to return to $100.

Can an account lose money even if wins and losses are the same percentage?

Yes. Each loss is taken from a larger balance than the following gain, so after repeated equal-percentage wins and losses, the account ends below its starting value, such as $90.44 after ten trades.

Is a losing streak proof that a strategy has stopped working?

No. The video explains that even a 55% or 70% win rate strategy commonly produces multi-trade losing streaks, so streaks are expected statistical behavior rather than evidence of failure.

Full Transcript — Download SRT & Markdown

Speaker A

Trading is all about math, and even with a good strategy and a high win rate, you can still lose almost your entire account. But once you understand these six mathematical concepts, you'll realize why having a profitable strategy is not enough, and it could change the way you trade forever. In this video, I'll break down 30 mathematical lessons across six parts: losses, streaks, ties, hidden risk, proof, and the plan. Let's start.

Speaker A

way you trade forever. In this video, I'll break down 30 mathematical lessons across six parts: losses, streaks, ties, hidden risk, proof, and the plan. Let's start. Now, my promise to you before we go to the video, I've already mentioned

Speaker A

Now, my promise to you before we go to the video: I've already mentioned we're going to go over 30 mathematical lessons. My promise is that at least 25 of these are going to be the first time you ever learn about, and they're going to shock you, and they're going to change the way you trade forever. And that is my promise. Let me know in the comments.

Speaker A

that is my promise. And let me know in the comments. And another thing is I already have two videos about the math, and each one goes specific into one thing in trading. So, this one here is about trading in general. This one here

Speaker A

Another thing is, I already have two videos about the math, and each one goes into specifics on one thing in trading. So this one here is about trading in general. This one here is about the math of prop firms, so it's applicable to prop firms in detail. And this one video that you're watching now is about one of the most important concepts in trading, and it's the one that makes you survive in the game and make money. So this one is going to be different.

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survive in the game and make money. So, this one is going to be different. Now, the first thing and the first shock you'll probably have is down is faster than up. And what that means is a loss takes a piece of your account, but a

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Now, the first thing, and the first shock you'll probably have, is that down is faster than up. What that means is a loss takes a piece of your account, but a gain has to rebuild it from a smaller base. If we look at this here, if you start with $100 and you lose 50%, you're losing $50 and you're now at $50. But if you make the same 50% gain, you're still $25 short of the $100 you started with, even though you made the same percentage. So the percentages are equal, but they act on different amounts, $100 and $50. So now you don't only need 50% to make the $50 back; you need 100% to actually get back to $100. So again, you lose half, and now you need to double just to get back, not just 50% but 100%.

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same 50% gain, you're still $25 short from the 100 that you started with, even though you made the same percentage here. So, the percentage are equal, but they act on different amounts, 100 and 50. So, now you don't only need 50% to

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So a 10% loss needs an 11% gain to get back to the original amount. A 25% loss needs 33%, and as you go to a 50% loss, you need 100%. At a 75% loss, you need an insane 300%.

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an 11% gain to go back to the original amount. -25% needs 33% and now as you go to -50% you actually need 100%. At -75% you need an insane +300%.

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Now, this line here is what it feels like it should be, but the reality is much more aggressive and much steeper. It becomes steeper as you go up, because every loss leaves a smaller amount of money available to produce the recovery. For example, if you're down 90%, you need to make an insane 900% just to go back to the original amount.

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So, for example, -90% if you're down 90% you actually need to make an insane 900% just to go back to the original amount.

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That is insane, because instead of having $100, you have only $10, and you need to bring it back to $100. You're now only working with $10, and that's a much smaller base to grow back to $100. That is the main difference here. And this is the formula you can use to calculate the gain needed: the required gain equals the loss divided by one minus the loss. That's exactly what the last graph is based on.

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$100. That is the main difference here. And that's the formula that you can use to actually calculate the gain needed.

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Now, let's talk about equal percentage wins and losses and how they still lose money. If you win 10% and lose 10% ten times each, you're actually still down 9.6%. The $100 first becomes $110, a 10% gain. Then losing 10% from there removes $11, not $10, leaving you at $99. If we keep doing this, no matter what the order is, after ten trades you always end up at $90.44. You're still losing money even though you're winning and losing the same percentage every time. The account falls because each loss is taken from a larger balance and each following gain starts from a smaller one. Notice how you're at $110 when you lose 10%, so you lose from that larger amount, and when you gain 10% from $99, you're gaining from a smaller amount than $100. Many people, especially beginners, don't understand this about risk, randomness, and the order of trades: if every 10% gain is followed by a 10% loss over and over, you're still down, not up. Not even break-even, but down.

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you're actually still down 9.6%. The $100 first becomes 110. That is a 10% gain. And then losing 10% from here removes an extra dollar. So, now you're at $99.

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Now, look at this, which is about the swings. What I mean by a swing here is the size of the movement around the average result. All three strategies here average plus 1% per trade. The first one has small swings. The other two move up and down more aggressively, and this one has 15% swings. With small swings, $100 grows to about $265. With the 2% swings, the account also grows to about $265. But with medium swings, it reaches $165, and with the largest swings, it falls to $89. Why? Because large movements create more compounding damage. A 50% gain followed by a 40% loss sounds positive on average, but $100 becomes $150 and then falls to $90, which is what we discussed in the previous example. So the average return is not enough; the size of the swings matters just as much.

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You're still down money even though you're winning and losing the same amount every time. And the account falls because the loss is taken from a larger balance and the following game starts from the smaller one. So, notice how

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Consider this coin game, which gains 50% on heads and loses 40% on tails. On average it pays 5% per flip. But after 50 flips, 76% of the players have lost money. Here are 46 players playing the same game. One heads and tails pair turns $100 into $90: $100 becomes $150 on heads, then a 40% loss on tails removes $60. After 50 flips, a few extremely lucky players became very wealthy and pulled the group average up to about $1,147. The typical player finishes with about $7, and the other 76% actually lost money. A high group average can hide the fact that most individuals are losing money.

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especially beginner, about the risk and the randomness and the order of the trades and how every 10% gain if you just do it over and over, you're still down and not up. Not even break even, but you're down. Now, look at it this

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Another thing that's going to shock a lot of you is that random results arrive in clusters. These 60 trades come from a strategy with a 55% win rate, and it still produces six consecutive losses. So even a good strategy often loses in a row. The streak is not a sign that the strategy stopped working; it's what a 55% win rate looks like. Even a 70% win rate will probably lose five in a row. Look at these numbers: the potential losing streaks compared to the win rate, specifically the longest losing streak to expect over 500 trades. We have two figures: a likely one, at 50/50 odds, and a bad case, at one in ten. At a 70% win rate, the likely longest streak is about five losses. At 50%, it's around eight, and in a bad case it could reach 11. At 40%, the bad case is 11, and at 30%, it can go up to 15. That could be a huge and painful streak, but the strategy can still be profitable. This is why risk must be sized for the longest streak the strategy may eventually face. If you know you could lose 15 times in a row, you should not use high risk per trade, because eventually you will lose your account. Think about it this way: at 10% risk per trade, five consecutive losses removes about 41% of the account. At 1% risk, the same streak removes about 5%. That's a big difference.

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down more aggressively and this one has a 15% swings. With small swings, $100 grows to about $265.

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On this visual, every line has the same edge, but some are making money, some are in the middle, and some are losing money. The only thing that changes is the order of the wins and losses. Here we're looking at 20 random runs of 200 trades with a 55% win rate and a 1:1 reward-to-risk ratio. The expected value is about 0.1R per trade. Every line has the same edge, and the only thing that changes is the order of the wins and losses and how they came in. It's based on 20 random runs of 200 trades, and this edge, a 55% win rate with a 1:1 reward-to-risk and an expected value of 0.1R per trade, is a profitable strategy. But sometimes you will do great, which is the expected outcome, and other times you will lose money even though it's a profitable strategy. Why does that happen? Simply because of the order of the trades. So sometimes you might actually...

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But with the largest one, the largest swings, it falls to 89. And why is that?

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Because large movements create more compounding damage. 50% gain followed by a 40% loss sounds positive on average, but 100 becomes 150 and then falls to 90. And that's what we've discussed on the previous one. So, the average [clears throat] return is not enough.

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The size of the swings matters as much. Now, assuming this coin game that actually gains 50% on heads and minus 40% on tails. So, simply it pays 5% per flip on average. But after 50 flips, 76 of the players have lost money. Let me

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show you how. And these are 46 players playing the same game, which is the coin flip one. Now, one heads and tails pair turns $100 into 90. 100 becomes 150. And then 40% loss removes 60. After 50 flips, a few extremely lucky players

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became very wealthy and pulled the group average up to about $1,147. Now, the typical player finishes with about $7 and the rest the 76% actually lost money. So, think about it this way, a high group average can hide

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the fact that most individuals are actually losing money because of the average. Now, another thing that's going to shock a lot of you, which is random results arrive in clusters. Now, these 60 trades that you're seeing now come

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from a strategy with a 55% win rate and still produces six consecutive losses here. So, that means even a good strategy actually loses together often.

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And the streak is not a sign that it stopped working. It's what actually 55% looks like. Now, even a 70% win rate will probably lose five in a row. And let's look at these here. The potential losses in a row are compared to the win

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rate. And we're looking at the longest losing streak to expect over 500 trades. And we have two. We have a likely one, which is 50/50, and a bad case, one in 10. So, at 70% win rate, the likely

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longest streak is about five losses. At 50%, it's around eight. When in a bad case, it could actually go to 11. 40, [clears throat] 11. And at 30%, it can go up to 15. That could be a huge one and a painful one.

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But, the strategy can still be profitable still. And this is why risk must be set for the streak the strategy may eventually face. So, if you can actually know that you could lose 15 times in a row, then you should not just

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go with a high risk because eventually you will lose your account. You think about it this way, a 10% risk per trade, five consecutive losses removes about 41% of the account. At 1% risk, the same streak removes about 5%. That is a big

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difference. Now, on this visual, every line has the same edge, but some are making money, some are maybe in the middle, and some are losing money even though it's the same edge. But the only thing that change is the order of the

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wins and losses and how they came in. So here we're looking at 20 random runs of 200 trades with 55% win rate and a 1:1 reward to risk. So the expected value is about 0.1R a trade. Now we have this

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visual here and every line that we're looking at has the same edge and the only thing that changes is the order of the wins and losses and how they came in. So we're looking at this model here.

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It's uh based on 20 random runs of 200 trades and this edge is a 55% win rate with a 1:1 reward to risk and an expected value of 0.1R a trade. So it's a profitable strategy here. But sometime

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you will do great. This is the expected and other times you will lose money even though it's actually a profitable one.

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So why is that happening? It's simply because of the order of the trades. So sometime you might actually start with a losing streak and then after that you might actually make money, but the order of the losing streak is going to come

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better early and you'll end up the 200 trades with a loss. But in the best scenario, when you're actually starting with the winners and you have some luck, you'll end up with a huge gain. And if we just zoom in here at the beginning,

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maybe after 20 trades, it does not mean anything. A short losing streak could mean nothing. After that we could make money. So I cannot say that it's good or not good based on the first few trades here. And that's what I wanted to go

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deeper into. So, a really each can still be losing after 100 trades. And we're looking here at the chance of a 55% strategy is below where it started.

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Short-term results are mostly noise. So, let's focus on this here. This video goes over the chance you're actually losing money after this many trades. So, after 20 trades, the chance is about 25%.

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After 100, it is still 14%. So, one in seven. And after 500 trades, it falls back to 1.1 and it's one in 90. So, again, a short losing streak is weak evidence that a strategy is bad. And in

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the same way, a short winning streak is weak evidence that it's actually good. You could actually spend almost nine of every 10 trades below your best day.

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First of all, a drawdown is a decline from the highest account value reached so far. If an account, for example, rises to $12,000 and falls to 10,800, this is a 10% drawdown. Now, the shaded area shows every period spent below the

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previous high. Across the simulation that we had, about 89% of trades happened during these periods below the highest amount that you had. And that does not mean 89% of trades lose, but it means recovery often takes many trades.

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So, even growing accounts spends most of its time below its latest peak. Now, talking about drawdown, your worst drawdown is still ahead of you. Now, the typical worst drawdown in this model is around 8R after about 100 trades, and

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then 13R after 500s, and 20R after 2,000. Now, the strategy has not become weaker just because the drawdown was going up, but it's about the longer trading history simply creates more opportunities for an unusually bad sequence to actually happen. And for the

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same reason, the worst drawdown in a back test is not a guaranteed limit. It's only the worst decline contained in that particular sample. For 1,500, you will have a specific one. For 1,000, you will have a specific one. And most

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likely, as you go more in trades, you have more potential drawdown. Now, let's talk about position size. And let me start with this. Size is the only thing you fully control. So, you cannot control the next trade. You can only

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control how much is allowed to cost and lose. With a $10,000 account and 1% risk, I can lose $100. If the distance from my entry to my stop is $2 per share, I divide my 100 by two and then

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buy 50 shares. The math decide this, and you decide this first. Now, let's look at this. Trader A uses a $2 stop and buys 50 shares. So, the loss if stopped is $100. Trader B uses a $5 stop and buy

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20 shares. Trader A can lose 50 multiplied by $2. Trader B can lose 20 multiplied by $5. Both risk equal $100.

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The number of shares alone does not tell us the risk. We need both the position size and the stop distance. In simple terms, size is equal the risk in dollars over the distance per unit. Now, this curve shows what happens as risk per

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trade increases. Now, growth initially rises because more money is exposed to the strategy's edge. Now, in this example, the expected growth peaks near 10% per risk, and this growth maximizing point is known as the Kelly size. Beyond that point, the damage from losses

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begins to overpower the extra profit from wins. Notice how the expected growth reaches near zero around 20% risk. So, actually, if you risk 20%, then you're most likely to actually reach zero. So, in simple terms, that means a winning strategy can lose money

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when the position size is too large. So, we need to find the one that fits the setup that we're having. And not go too big and not too small. And now here we're looking at three accounts taking the same 300 trades and win the same 165

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wins. Now, for this one, we're looking at the same 300 trades winning 165 times and losing 135. And this is a 55% win rate. We're looking at 10% risk, 1% risk, and 25% risk. Both the traders with a 1% risk and 10% risk made money.

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But, then the one risking 25% actually lost 87% of the account when the trader risking 1% made 33%. But, the guy that is risking a bit more, which is 10%, is making much more, 349%.

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So, here nothing changed except the amount risk. Large losses repeatedly reduce the account base leaving less money for the later wins to rebuild.

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Now, you might be asking, "Why not just risk too much?" And everyone is talking about the 1% risk, 2% risk, and not more than that. Simply because the perfect size comes with an 83% drawdown. And it's actually grows the fastest on

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paper, but almost no human can sit through. You cannot, you know, stand an 83% drawdown. And that's why professional traders use it just a fraction of it. So, at 1% risk per trade, the typical worst drawdown is about 13%. At 5% risk, it reaches 53%

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drawdown, and that's insane. At 10% Kelly size, it reaches roughly 83%, and that is actually the perfect size, but the drawdown is huge. But it's rarely financially or emotionally practical. Traders therefore tend to use only a fraction of the theoretical

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maximum. Now, there is a type of strategy that actually doubles the position after every loss so that one future win can recover the sequence. And the bets grow from one unit to two to four to eight, eventually 512 units by

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the 10th loss. Now, the total loss reaches 1,023 units, all in pursuit of one unit profit. This method produce frequent small wins, but one ordinary long losing streak can erase everything. So, in simple terms, this style of trading does

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not work and it's better to actually just stick to one percentage, or even better, what I'll discuss on the next sections. Now, the iceberg shows the risk we can see and those we may overlook. Above the waterline are the

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entry, the stop loss, and the position size. But below it are correlation, the trades that move together. We have gaps, a price jumps past your stop, and we have the fat tails, the huge moves far too often, and then leverage, less room

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to be wrong. Each one can make a 1% trade cost far more than 1%. Now, let's cover correlation here. So, five trades at 1% can be one trade at 5%. What does that mean? Now, first of all, correlation measures how closely markets

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move together. A value close or near zero means their movement are mostly unrelated. A value near one means they move almost identically. Now, here we're looking at five markets move together.

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The correlation. Now, risking 1% each behave like roughly 2.2% of combined risk. The moderate correlation that rises about 3.9% and if all five move together, the full 5% can be lost all at once. Owning five technology stocks, for example, may look

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diversified, but if all five react to the same interest rate news, they're effectively one larger technology position. So, you simply lose them all at once because the correlation is almost identical. Now, we've talked about the only thing that you can

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control, which is risk. And one of the thing we can see the risk is a stop loss. Now, a stop loss is actually an order and not a promise. Now, the position is supposed to exit at minus one R, that is your stop. But, the

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market closes before reaching the stop and the reopens far below it. Now, the stop activates, but the intended price is no longer available. The trade is filled at the next available price, creating instead of a minus one R loss,

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you're actually getting a minus four R loss. The difference between the expected and the actual price is slippage. Gaps can make it especially large because the market moves across several prices without trading at them.

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Now, you've all heard about this when they said, "This happens once in 7,000 years or in a thousand year or it did not happen since 1960." But, the reality is different. Extreme moves happen more often than basic models predict. For

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example, a bell curve assumed that most market moves stay near the average and extreme moves are exceptionally rare.

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Now, under that model, a five sigma move should occur about once every 6,900 years. A fat tailed model, which allows the extreme outcomes more often, produces a similar move roughly every 15 months. The exact timing is not the

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point. The point is that real markets produce unusually large movements far more often than a simple bell curve suggests. Notice the big difference here between the gray one and the orange one.

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A huge difference. Instead of 1.5 years, it's around 3 months. Now, leverage reduces the distance to failure. Now, what I mean by leverage and the meaning of it is controlling a position larger than the account. With $10,000 and a 1:1 leverage, I control the

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$10,000. But at 100:1, I control $1 million. Now, a 1% move against that $1 million equals $10,000, the entire account. Now, at 500:1, only a 0.2% move is needed to actually just wipe out the account. So, leverage does not

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change the market, but it multiplies the effect of the market's movement on the account. Now, every result is edge plus luck. Now, suppose a strategy expects to earn positive 0.1R per trade. After 20 trades, the edge contributes only about

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2R, while random variation or luck can move the result by roughly 9R in either direction. Strong profit or loss at this stage may mostly be luck. But after 1,000 trades, the accumulated edge reaches 100R. Randomness still matter, if you notice here, but it's smaller

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relative to the expected profit. So, a real edge becomes easier to identify as the sample grows. And if you want to do the math, it's right here. Now, if you've been trading for a while, you would know that a lot of traders

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actually compare trading to coin flipping. So, let's understand this. If you give 100 people a fair coin and 20 flips each, about 25% of them will get 12 or more heads, giving them a 60% win rate or better. Some may appear

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exceptionally skilled even though every participant has exactly the same zero edge method. They don't have an edge.

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So, because we're doing this on 20 trades, the sample is small and many people are actually participating. A few emperor's of records will appear by chance. So, all of this is luck. So, simply one in four coin flippers will

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look like a 60% traders. They have a 60% win rate. When in reality, they don't even have an edge.

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After 50 trades, a 60% win rate could be anything from 46 to 74%. This might be weird, but let me show you based on math. So, in simple terms, your true win rate is hiding somewhere inside the red

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and it only gets narrow and more specific after hundreds of trades. Because with so little data, the strategy's true win probability could reasonably be anywhere from about 39 to 81%.

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But at 500 trades, the estimated range narrows to roughly 56% to 64%. So, it's getting closer to the claimed one, but only after a lot of data and not a small sample. So, this range represent uncertainty. The measured result become

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more precise as more trades are observed. You notice how it gets narrow as we have more trades. Now, let's talk about edge and luck because they are very related to each other. Now, the straight line we have here is the

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expected profit from an edge of 0.1 R trade. And the surrounding bands, this and this, show the range that normal luck can create. Now, early on, the luck band is much larger than the expected profit. The lower edge of that band only

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moves about zero, but if we compare it to the bad luck or the lower one than our band, bad luck can no longer hide the edge. Before then, a profitable strategy can easily appear unprofitable because the edge is still small compared

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with the noise. Now, the smaller your edge, the longer you must survive before anyone can tell if it's real, including you. An edge of 0.2R becomes visible after about 100 trades. And then if we look at 0.05R, we're looking at 1,600 trades before

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luck can't hide it. Now, comparing these two numbers, you will notice that if you cut the edge by half, so instead of 0.2 you go with 0.1, you actually need 4x the amount of trades to actually make the edge visible. So, small edges can be

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valuable, okay, as we go smaller, but they are difficult to prove quickly. You need much more time to actually prove them. Now, we're looking at the part that actually matters. Now, we have several layers of limits. The first one,

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for example, controls one trade. So, how much can the single idea cost? Now, the second controls the day. So, you ask yourself, "After how much loss do I stop trading?" For example, 3R. And then per week, you're simply preventing several

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bad days from becoming a much larger problem. And the final limit protects the account by defining when position size must be reduced or trading must be paused. Each layer catches something the previous one cannot. And these limits should be written while calm before

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losses begin affecting decisions. Now, the original system here earns positive 0.2R per trade. Same entry, same market, and only small habits that change that can actually turn a winning system into a losing one. So, how does this happen?

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Now, when you move your stop, this one removes around 0.08R. And then taking profits early takes this amount. Costs and slippage takes this amount. And then at this point, what you get is a losing system. So, it was a

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profitable one, but then you keep losing and you keep doing the small habits and after a while you're just at minus 0.05 R and you are not trading a profitable system. Now, one of the most important things that you can do when you're going

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into a losing streak or period that you actually don't know what you're doing and something is going on with the market, what you can do is trade smaller and that's going to make that disaster disappears and it removes almost all of

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the the worst outcomes. Now, the dark bar shows what happened when you always risk 2%. The light one, the orange, it shows you that when you go smaller when losing. Now, first let's look at the growth. So, the fixed 2% risk is

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actually producing much more growth, a 146% compared to 84%, but then when we look at the bad case drawdown, one in 10 worst. In this case, if you go smaller, you're actually going to be losing 21% instead of 36% drawdown. And then

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looking at the chance of a 30% drawdown, it goes from if you're actually risking 2%, it's a 25% chance of reaching 30% drawdown. But, if you go smaller when losing, then it's going to be near 0%.

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The rule gives up some upside in exchange for a much lower chance of a severe damage that you cannot recover from. Now, finally, I want you to think about surviving first and then the edge will do the rest. So, let's look at some

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tips here that's going to help you a lot. First of all, when it comes to losses, you need to protect the downside first. Why? Because a 50% loss needs 100%. So, if you can [clears throat] control the downside, then you will not

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need to go through this. And then you plan for the streak before it comes because a 70% win rate can actually have five losses in a row. And then make sure to actually follow the right size because past the peak, more size means

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less money. It's not always about more money. And then correlated trades are one trade. Five linked 1% trades equal 5%. So, if you lose one, you're probably going to lose all of them, and it's going to be a 5% loss. That's not

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diversification. And then judge your strategy by hundreds of trades, because 20 trades, 30 trades are just noise. And write the limits down before you trade.

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And cut size in drawdowns as we discussed earlier. That's it for this video. I really hope you enjoyed it.

Speaker A

Make sure to leave a comment, hit the like button. I really appreciate you. If you actually like the video, then make sure to do that. If not, it's all okay.

Speaker A

Feel free to check out H-School, my community, and my trading strategy after 8 years, all based on one week. That's it, and I'll see you in the next one.

Topics:trading mathdrawdownposition sizingrisk managementcompoundingwinning streakslosing streakstrading psychologyexpected valueportfolio correlation

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