What is the best way to construct investment portfolios: based on asset prices or based on the changes in asset prices through time? E.g., if Asset A is 55 in 2010 and 60 in 2011, should I use 55 and 60 as data points or should I use 5 (i.e, 60 minus 55)? Thank you in advance.
Usually investment portfolios are built using asset returns, not prices. Say besides your asset A there's an asset B that moves from 100 to 60, an equally weighted investment portfolios would return 0.50 * ((60-55)/55) + 0.50*((60-100)/100) = -0.1545455 or about -15.4%. The cumulative performance, i.e. what you end up with, is then 1-15.4% or about 84.6%.
If you have multiple periods, you'd then compound returns by multiplying them.
Another very common way to approach this issue is to use log returns. Have a look here: https://quantivity.wordpress.com/2011/02/21/why-log-returns/
hi Thales A.P. West
have also a look here: https://www.r-bloggers.com/cointegration-correlation-and-log-returns/ for return vs price.
Financial asset prices suffer from stationarity issues. There is no "natural law" that will contain asset prices within ranges therefore if you look at asset returns only to compare/differentiate two asset you might be missing the "big direction" changes between them.
That's why practitioners like to separate in "common" buckets/clusters first such as similar country or similar business sector. Then within the "common" buckets or clusters look at the return differences.
Then if you want to construct a "base" portfolio there is the CAPM -> https://www.investopedia.com/terms/c/capm.asp. Often you start with asset characteristics to build portfolios (Market cap - liquidity). But that is a proxy of the "market". Then you tweak the "market" portfolio to match your investment/anticipation preferences.
hope it helps
cheers, T
Is there any literature on this topic? In some capm models I see series like Pt / Pt-1 or perhaps you can use logPt
Jan Jansen there is a chapter on "Fractionally Differentiated Features" in Lopez de Prado's "Advances in Financial Machine Learning". It deals with the trade-off between making time-series stationary by using returns and the memory-loss that is generated by doing so.
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