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3

What @noob2 said: Actually there is empirical evidence of the opposite, i.e. the existence of a Term Premium. But this is not evidence of arbitrage, just that a more complicated risk model than assumed here is needed. And the simpler theory is still useful in many ways I feel it's helpful to unpack this a little. Let's say you are buying a 10 year Treasury/...

1

Forwards and futures only need to agree on price in a world with deterministic interest rates as a general rule (it is possible to cook up examples of random rate models where the correlation between the underlying and the rate process force the same relationship but they are rather contrived). That covers the general case but your questions revolves around ...

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Irrespective of current stock price, the price of the 90 Call option should be 8 given the probability of payoff. Think, if the probability of price will be at 100 was 100%, then the call price will be 10, again irrespective where the stock price is.

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Assuming that the only things that can happen on the period are $100$ and $50$, and we can buy a stock and a call option with strike $90$, even without knowing the probabilities of these moves we can relate the price of the stock $S$ and the option $C$ If we buy $0.2 S$ and sell one call option $C$, we have a portfolio that will be worth $10$ in either end-...

3

Under the risk-neutral measure by application of Ito: $$dS^3_t = 3 \left[ (r + \sigma^2)S^3_t dt + \sigma S^3_t dW_t \right]$$ The risk-neutral drift is not the risk-free rate and hence $S_t^3 \; \forall t$ cannot be the price of a claim or any other tradable asset. So basically along the same lines as your proof, but without calculating expectations etc. ...

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There's a lot to pick apart here, but to start: (1) Holding period on your two strategies? A Sharpe of 2.8 is quite high (like, top decile+) for a long-only buy and hold mid to low frequency equity strategy. Even .9 is on the high side for a broad-based US index. (2) Using 70-90 as a training set and 95-present as an out of sample set seems prime for ...

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