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I've never delved into short selling much since it is not available for IRAs. But recently i've had the desire to run some Excel calculations on shorts, and i've run into a problem.

I'm trying to take daily returns and find out the overall compounded return over some time period as if a position was held short. I thought inverting the daily returns and taking the product of them would give me the return as if the position was held short, but that doesn't seem to be working. I'm getting different values for overall return than if I had simply took the start price and end price and calculated the return from the short position that way. Would anyone happen to have some insight into what i'm doing wrong?

ie:
Day 1 price: \$10
Day 2 price: \$12 (20% return or 0.20)
Day 3 price: \$11 (-8.33% return or -0.0833)
A \$100 short position: \$100/\$10 = 10 shares. Buy back at day 3: \$11*10=\$110. \$100-\$110= -\$10 loss or 10/100 = -10% loss.

But if I invert the return to get: -0.20 and +0.0833, add one to get: 0.80 and 1.0833. Take the product, I get: 0.866 or a -13.4% loss.