Portfolio Selection and Risk Management

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Taught by
Arzu Ozoguz
Finance Faculty
and 7 more instructors

Offered by
Rice University

Reddit Posts and Comments

0 posts • 1 mentions • top 1 shown below

r/CryptoCurrency • post
124 points • Hotsiam
Diversification in Cryptocurrencies is only effective with holdings of more than 4-5 (max 20-30) coins, with a weighted Correlation Coefficient of -1

For quite a while now the mantra in the crypto community has been to "make sure you diversify". Ultimately there is some element of truth to this, but in practice I see a lot of people implementing this as a rule of thumb rather than as a function of modern portfolio theory. Which is the whole reason why so many people unwittingly suggest diversification in the first place.

There is absolutely no point in diversifying, unless there are strong fundamental themes driving your decisions to diversify (which I wouldn't recommend on it's own, due to degree of subjectivity of opinion) and/OR you're using the following steps based on modern portfolio theory:

Step 1.0

Identify the coins that you're interested in and define their correlation coefficients:

The premise behind this is that the closer you get to -1 in c/coefficient the larger the degree of variance in market behaviour between the cryptos in question. Where, for example, participants aren't just buying or selling as a function of Bitcoin price.

The following website is really good for identifying negatively correlating crytpo's: https://www.sifrdata.com/cryptocurrency-correlation-matrix/

Step 1.1

Devise a model of weighting (e.g. Crpto A = 50% of portfolio; crypto B = 50% of portfolio). There is no right or wrong way to distribute your portfolio but I personally do it based on my fundamental convictions (i.e. Nano = 40% of portfolio; ETH = 50%; XMR = 10% etc). The theory suggests that 2-3 won't really bring about much reduction in risk, but the closer you head towards a portfolio with 20-30 different cryptos, the greater the degree of reduction in risk. I also revise this decision after Step 4.1

Step 2.

Identify historical returns of the coins that you're interested in for period x: (this could be weeks, months, years it really just depends on your needs as an investor/trader. although the greater the time the greater the uncertainty).

Step 3.

Figuring out the average return for the chosen period:

(x+y+z)/3 = return = (10%+(-10%)+20%)/3 = 3% for e.g. monthly periods, over a 3 month timeframe.

Step 4.0

Risk in terms of standard deviation:

you can identify what the risk is by figuring out the square root of the sum of periodic returns (-) minus the return of the average weighted return ( ^ ) to the power of 2 ( / ) divided by the number of periods. Just wiki standard deviation formulas to get the proper notation.

Alternatively, this short video is pretty useful https://www.coursera.org/learn/portfolio-selection-risk-management/lecture/yQp1s/diversification-a-graphical-illustration-with-two-assets

Step 4.1

get the risk in terms of variance: which is risk in terms of standard deviation ( ^ ) to the power of 2.

note: after this step it is worth re-thinking the weighting of your portfolio allocation, to narrow down the best possibilities. I would consider weighting my portfolio allocation based on the risk in terms of variance, but at the end of the day figuring out the best portfolio weighting is really just trial and error.

Step 5.

Figure out the portfolio return using the weighted average of individual returns: R = (size of portfolio share % for crypto A) x (weighted average return for crypto A) + (size of portfolio share % for crypto B) x (return for crypto B).

Step 6.

Identify the sum of the weighted average risk in portfolio A multiplied by the correlation coefficient:

risk = (portfolio share of crypto A) ^ 2 * (risk in crypto A) ^ 2 + (portfolio share of crypto B) ^ 2 * (risk in crypto B) ^ 2 + (2 * correlation coefficient * portfolio share of crypto A % * portfolio share of crypto B % * risk in crypto A * risk in crypto B).

Remember risk = standard deviation, and the closer your correlation coefficient is to -1 the better chances you'll have of diversifying your portfolio. Hence, a significant reduction in risk.


If you follow these steps it will give you way greater edge over the average crypto investor, because it will allow you to identify the ideal amount of risk, as well as risk reduction, for the maximum amount of return, the Efficient Frontier of portfolio management.

ie. portfolio A-B (sharing 50:50) gives returns of 9%, but a risk of 7%; while portfolio D-E (sharing 20:80) gives returns of 8% but only a risk of 3%. From a rational investing POV it is far more sensible to go with portfolio D-E because you're getting slightly less returns in exchange for a significant reduction in risk.

The best way to calculate risk and return as a function of the correlation coefficient is to use Excel. this is because you can model and replicate the calculation using 100s of different portfolio structures and narrow down the ideal composition for diversification.

I'm currently in the process of programming a website/app with this model embedded for cryptocurrencies but if you search hard enough on google I'm sure you'll find someone who has uploaded their own excel templates, that you can use.

I just think we need more education like this in the crypto community, because at the moment it's just one giant shit show of weekly "don't kill yourself" threads, and a week later "buckle up, we're going to the moon". Surely education will lead to better market decisions and hence greater market stability in the long run.

Edit: Copping a lot of flack in here for sharing a theory/model that has been tested and verified over hundreds of years worth of data. If you guys go and test this model for the crash/dip period for crypto currencies, I guarantee you will discover that portfolios (comprised of more than 5, and maximum of 30 cryptos) with correlation coefficients as close to -1 as possible, suffered, on average, the least amount of losses for this period.

If you’re investing money in cryptos that you’d prefer to keep rather than lose then definitely use this model.