# Time and asset weighted rate of return of a portfolio

If I have a portfolio with 3 initial assets on day 1 (say, stock 1 with beginning market value of \$100, stock 2 \$150 and stock 3 \$175) and after 10 days the stock 2 is sold for \$200, how can I calculate the return of the portfolio after 30 days, assuming that stock 1 is now costing \$150 and stock 3 \$200?

• To compute a TWR (time weighted return) would require knowing the value of the 2 other stocks on day 10. Alternatively you could compute an MWR (money weighted rate of return) also known as IRR (internal rate of return) if you assume the \$200 is returned to investors on day 10 (you could also assume that the 200 is kept and reinvested in Tbills, etc.). TWR is the standard for investment management calculations, but it can't be computed with the information you gave. – noob2 Apr 15 '20 at 20:11 • If we assume that on day 10 the value of stock 1 is \$125 and stock 3 \\$190, how do we proceed to calculate the return on day 30? – Ken Apr 15 '20 at 20:20
• First period: (100,150,175) turns into (125,200,190), so that's 425 turns into 515, a return of 21.176%. Second period (125,nil,190) turns into (150,nil,200) or 315 turns into 350, a return of 11.111%. for the overall return we link these two returns together and get 1.21176*1.11111-1 = 34.640% time weighted return. – noob2 Apr 15 '20 at 20:28
• Is there a way to calculate this by analyzing the assets individually instead of calculating the net asset value of the portfolio as a whole? I mean, using only the individual return of each asset, in this case the problem would be the stock 2... – Ken Apr 15 '20 at 20:35
• In that case, you would simply write the last value (i.e. 200) forward and compute an overall return of (150,200,200) / (100,150,175). If you want to compute your returns on a per-investment basis, you would have to fix your initial portfolio composition (weights, i.e. 23%,35%, 41%) and use those to weight your per-investment returns (5%,33%,43%) ; arriving at 29.4% total return (assuming stock 2 is held in cash) – Kermittfrog Apr 16 '20 at 9:22