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Vic's Finance-Math Page

Some papers and expositions

• Notional portfolios and normalized linear returns (28-Apr-2011, PDF 167 KB)
  The vector of periodic, compound returns of a typical investment portfolio is almost never a convex combination of the return vectors of the securities in the portfolio. As a result the ex post version of Harry Markowitz's "standard mean-variance portfolio selection model" does not apply to compound return data. We propose using notional portfolios and normalized linear returns to remedy this problem.
      Also at <http://arXiv.org/abs/1104.5393>.
• Adjusted closing prices (21-May-2010, PDF 172 KB)
  Historical returns depend on historical closing prices and distributions. We describe how to compute adjusted closing prices from price/distribution data with an emphasis on spreadsheet implementation. Then the growth of a security from one date to another (1 + total return) is just the ratio of the corresponding adjusted closing prices.
• Some problems with the Markowitz mean-variance model
  (27-Jul-2009, PDF 142 KB)
  Harry Markowitz's mean-variance model for portfolio choice posits a linear relationship between the return of a portfolio and the returns of its component securities. This linear relationship does not hold in an ex post setting when monthly or quarterly returns are used.
• Notional prices and Markowitz's portfolio selection model
  (04-Apr-2009, PDF 100 KB)
• Sharpe-Optimal SPDR Portfolios
• A linear algebra exercise (28-Mar-2008, PDF 59 KB)
• Geometric Series and Motorcycle Racing (31-Aug-2007, PDF 296 KB)
Everybody knows that
    1/3 = 0.33333.....
The right-hand side of this equation is a simple example of a geometric series with ratio 1/10. In motorcycle racing a rider can qualify to race only if he can complete a lap within a fixed percentage (e.g. 10%) of the time required by the fastest rider. So how often (in laps) does the fastest rider lap a borderline qualifier during the race? This is a natural application of geometric series. For our 10% example the answer is every 11 laps.
• Two Funds Optimization
• The Geometry of Risk and Reward
• How to do average cost computations on mutual fund records.
• Computing rates of return for a mutual fund portfolio.

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Last updated: 5-May-11