Portfolio Optimization

[MG2014]

There are lots of discussions here about kelly criterion, but does anyone here use mean variance portfolio optimization or conditional value at risk when determining position sizing?

 

From what I've gathered in the last couple days of reading about this, to determine the optimal portfolio of a group of assets, typically the probability distribution of past returns for each holding is feed into MV or CVaR optimization to come up with the optimal position weights.

 

I'm wondering if instead of using past returns, one could come up with probability distributions of intrinsic values for each holding (based on their best guess), use the current stocks' prices to make that into a probability distributions of expected returns, then feed those into the model?

 

For example, let's say you've decided that two stocks have an intrinsic value that is some probability distribution with $10 being the most probable intrinsic value. They're both currently trading at $5. You decide to size each at 50%.

 

Then Stock A moves down to $3 and Stock B moves up to $7. Your view on the intrinsic value probability distribution hasn't changed, but Stock A now has a higher probability of increasing to fair value (Price is further left on the intrinsic value distribution) and Stock B has a lower probability of increasing. So you sell some of Stock B and use those funds to buy more Stock A. But what should the new weights be? And what if you have 20 holdings and not 2?

 

This is why I'm interested in applying CVaR optimization (MV optimization assumes normally distributed return distribution - not generally true), but I'm not sure if there's a different method? Or if this even makes any sense to someone who's done this before?

[wachtwoord]

Be careful with Kelly as Kelly assumed all 'bets' (stock picks here) are independent. This almost never the case, unless we're talking micro caps from different geographical regions operating in different markets. By all means use Kelly as a source of additional information but don't trust the outcome blindly.

[HWWProject]

I developed an optimization method that utilizes Kelly, Sharpe ratio and projected returns to determine position sizing among assets.  Asset classes are those suggested by work of Markowitz.  More description here:

 

http://healthywealthywiseproject.com/optimal-asset-allocation/

 

I adjust portfolio twice a year.  Been pleased with results first two years, and am more confident that I'm putting more money into asset classes which offer greater risk-adjusted returns.

 

more info on my thoughts on Kelly (I adjust Kelly results for stock market as suggested by Ed Thorpe)

 

http://healthywealthywiseproject.com/research-offers/the-kelly-formula-for-stock-investing-growth-optimized-money-management/

 

 

 

 

 

[moneyball]

HWW Took a quick look at your page. Just interested, how did you come up with your projections for asset class returns?

[Graham Osborn]

There are lots of discussions here about kelly criterion, but does anyone here use mean variance portfolio optimization or conditional value at risk when determining position sizing?

 

From what I've gathered in the last couple days of reading about this, to determine the optimal portfolio of a group of assets, typically the probability distribution of past returns for each holding is feed into MV or CVaR optimization to come up with the optimal position weights.

 

I'm wondering if instead of using past returns, one could come up with probability distributions of intrinsic values for each holding (based on their best guess), use the current stocks' prices to make that into a probability distributions of expected returns, then feed those into the model?

 

For example, let's say you've decided that two stocks have an intrinsic value that is some probability distribution with $10 being the most probable intrinsic value. They're both currently trading at $5. You decide to size each at 50%.

 

Then Stock A moves down to $3 and Stock B moves up to $7. Your view on the intrinsic value probability distribution hasn't changed, but Stock A now has a higher probability of increasing to fair value (Price is further left on the intrinsic value distribution) and Stock B has a lower probability of increasing. So you sell some of Stock B and use those funds to buy more Stock A. But what should the new weights be? And what if you have 20 holdings and not 2?

 

This is why I'm interested in applying CVaR optimization (MV optimization assumes normally distributed return distribution - not generally true), but I'm not sure if there's a different method? Or if this even makes any sense to someone who's done this before?

 

JMO here.  If you complicate/ quantify too much somethings the methods become self-justifying and you make high-level errors.  I always need a fundamental, macro, and technical justification for a trade.  Just realize you are cutting out two here, although I guess pure value investors might make the same call.

[MG2014]

I developed an optimization method that utilizes Kelly, Sharpe ratio and projected returns to determine position sizing among assets.  Asset classes are those suggested by work of Markowitz.  More description here:

 

http://healthywealthywiseproject.com/optimal-asset-allocation/

 

I adjust portfolio twice a year.  Been pleased with results first two years, and am more confident that I'm putting more money into asset classes which offer greater risk-adjusted returns.

 

more info on my thoughts on Kelly (I adjust Kelly results for stock market as suggested by Ed Thorpe)

 

http://healthywealthywiseproject.com/research-offers/the-kelly-formula-for-stock-investing-growth-optimized-money-management/

 

Thanks for sharing HWW

 

The problem with Kelly's formula is gives you the optimal bets for a discrete outcome case instead of a portfolio of holdings (ie. playing 25 single hands of poker consecutively vs. playing 25 hands of poker all at the same time and distributing your bankroll across all hands to match your expected risk/returns from each hand). I'll check out Thorp's paper.

 

JMO here.  If you complicate/ quantify too much somethings the methods become self-justifying and you make high-level errors.  I always need a fundamental, macro, and technical justification for a trade.  Just realize you are cutting out two here, although I guess pure value investors might make the same call.

 

Interesting point, can you elaborate? How do you take those into account? And what's a JMO?

 

 

[moneyball]

"just my opinion"

[frommi]

The problem is that the stock market doesn't work that way. A stock on the move up will probably close the gap to intrinsic value faster than the stock that is moving in the opposite direction. And without knowing the time a stock needs to reach intrinsic value you don't know your rate of return a priori.

 

[MG2014]

The problem is that the stock market doesn't work that way. A stock on the move up will probably close the gap to intrinsic value faster than the stock that is moving in the opposite direction. And without knowing the time a stock needs to reach intrinsic value you don't know your rate of return a priori.

 

True, but you never know the stock with the highest rate of return ahead of time otherwise you'd put all your money in that. Before optimization you've already decided these are your favorite undervalued 20 stocks that you believe will meet your personal return requirements in the next x years. Now you're just trying to optimize their sizing to potentially exceed that return requirement. If the price goes down, you would have a better range of expected returns for the stock moving in the opposite direction (as long as the thesis doesn't change).

 

I'm basically trying to answer "by how much" do I sell a stock that's closer to fair value and add more to a cheaper one. Something we all do already, I just think it would be interesting to formalize it.