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Kalman filter (or similar methods) are quite well suited to deal with observations that are of different sampling frequencies and/or asynchronous.

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In: MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS - ELTON, GRUBER, BROWN, GOETZMANN , chapter 5, you can find a good explanation of your issues.

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Portfolio return is simply weighted return of parts (and NOT the formula mentioned in your post) - e.g. if you invested \$100 total equally among the four funds (\$25 each), and each of those funds earned 1% on average, then on aggregate you made 1% return on \\$100 and not 4%. The trick (and the answer to your Q) lies in how you calculate these weights!! ...

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Financial markets & Corporate Strategy - Grinblatt & Titman The book is very intuitive, but as a consequence less comprehensive than ex. Options, Futures, and other Derivatives by Hull (which is seen as the basic foundation of everything quant in some parts of the industry.) A great entry level book to finance, and is publically avaliable here: ...

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If I had to give only one title this would be it: FT Guide to Understanding Finance by J. Estrada (Second Edition published 2011) It explains all of the above concepts (and more) in a very accessible, yet mathematically correct manner. A sample can be found: Here The only thing is that it is not really short (the first part, i.e. up to p. 150, is ...

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