There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of -
- market expectation of future short-term interest rates;
- bond risk premium: usually positive, longer duration bonds are more volatile and riskier, so investors demand a compensation in the form of higher yields;
Let's consider a case where market expectation is flat (people don't think interest rate will rise or fall in the next 10 years) and bond risk premium is zero. You may think the yield should be flat, but it actually would still be inverted. This is because longer term bonds have higher convexity, so investors are willing to accept a lower yield in order to gain this "convexity advantage."
Now consider a world where convexity isn't considered valuable and market expectation is still flat, but bond risk premium can be negative, causing the yield curve to invert. Throughout much of 2012 and 2013, US bond risk premium was indeed negative, partially because of QE, and partially because of flight-to-quality flows (Europe was blowing up!)
Finally, the yield curve can be downward sloping because the market expects interest rate to decline in the future.
I'm not sure why you think there's an arbitrage when the curve is inverted. Consider a scenario where 1-year rate is 5% and 10-year rate is 4%. An investor then purchases the 1-year note purely because of yield considerations. But there's no reason why the yield curve can't flatten more. Let's say 1-year rate rises to 6% (maybe because the Fed keeps hiking short-term policy rates), and 10-year rate declines to 3.5% (perhaps because of Foreign central bank buying). In this case, the 1-year bond LOSES money, while the 10-year bond actually makes money.