Expected daily return given binary outcome

Question

Every day a trader either makes $50$% with probability $0.6$ or loses $50$% with probability $0.4$.

The average return per day is: $1-\exp (0.6 \ln 1.5+0.4 \ln 0.5)=-3.34 \%$

How is this average calculated?

Answer 1

I would have calculated the average return like this:

0.5 * 0.6 - 0.5 * 0.4 = 0.3 - 0.2 = 0.1, or 10%.

This means in the long run, the trader makes an average of 10% return each day. Since the probability of makes 50% is higher than that of loses 50%, the average return can't be a negative number.