Hi,

I was recently going through this lecture on Arbitrage Pricing Theory, and got stuck with this example.

**Arbitrage
Now that we have a reasonably general way to compute expected return, we can discuss arbitrage more technically. There are generally many, many securities in our universe. If we use different ones to compute the {λi} , will our results be consistent? If our results are inconsistent, there is an arbitrage opportunity (in expectation), an operation that earns a profit without incurring risk and with no net investment of money. In this case, we mean that there is a risk-free operation with expected positive return that requires no net investment. It occurs when expectations of returns are inconsistent, i.e. risk is not priced consistently across securities.
Say that there is an asset with expected rate of return 0.2 for the next year and a β of 1.2 with the market, while the market is expected to have a rate of return of 0.1, and the risk-free rate on 1-year bonds is 0.05. Then the APT model tells us that the expected rate of return on the asset should be
RF+βλ=0.05+1.2(0.1−0.05)=0.11

This does not agree with the prediction that the asset will have a rate of return of 0.2. So, if we buy $100 of our asset, short $120 of the market, and buy $20 of bonds, we will have invested no net money and are not exposed to any systematic risk (we are market-neutral), but we expect to earn 0.2(100)−0.1(120)+0.05(20)=9 dollars at the end of the year.**

My questions are as following:
1. The calculated expected rate of return is 0.11, why do we say that the predicted rate of return on the asset was 0.2?
2. The expected rate of return 0.11 is less than 0.2, so why are we shorting the market? Given that we expect a lower return on the asset of our interest, shouldn't we short the asset we have instead of buying it?
3. Where does the amount $120 come?: $100 to buy our asset, $120 to short the market, and $20 to buy bonds. Is the number arbitrary?