Why Stock Portfolio Weights Do Not Transfer Directly to Calls
Summary
The document considers replacing a diversified stock portfolio with long-dated calls on the same companies, keeping the same percentage allocation across names. It asks whether diversification carries over and what additional risks the options introduce. The response distinguishes diversification of underlying-specific shocks from the expected performance of the instruments: spreading exposure may reduce the impact of a shock isolated to one company, but it does not remove the cost of option time decay or the need for prices to move enough, soon enough, relative to each strike.
The answer argues that a diversified long-call portfolio can still lose value over time even if its holdings are spread across several stocks, while diversification can help contain concentrated shocks. It offers no quantitative analysis, option pricing comparison, or evidence for its broad claim that options generally decline in value. Outcomes depend on strike, maturity, implied volatility, premiums, and the strategy’s expected returns; the passage does not assess these factors. Its discussion of short options is only a brief contrast, not a complete alternative strategy.
Key ideas
- Keeping the same percentage weights across calls does not preserve the stock portfolio’s risk and return profile.
- Diversification can reduce the effect of shocks concentrated in a single underlying.
- Long calls require favorable movement relative to both strike and expiration, and their premiums can decay with time.
- The response warns of persistent losses in diversified long-option portfolios but provides no quantitative evidence.
- Option outcomes depend on contract terms, volatility, premiums, and the underlying strategy’s edge.
Tags
Full text
# Is there a sound logic for buying a portfolio of call options in the same ratio as you would buy the underlying shares? # Is there a sound logic for buying a portfolio of call options in the same ratio as you would buy the underlying shares? Suppose I believe it would be profitable to build an investment portfolio by investing, say, USD 30,000 in stocks in the following ratio: 30% in shares of CompanyA, 30% in CompanyB and 40% in CompanyC. Say that my analysis shows that over the past 10 years, these stocks have performed well as a portfolio, and have a Sharpe ratio of, for example 1,50. Suppose further that I consider two different strategies. Strategy 1: invest USD 30,000 directly in the stocks in the ratio mentioned above: 30% A, 30% B and 40% C. Strategy 2: Instead of investing in the shares of these companies I, would buy long term call options (with a maturity of say 2 years) on these same shares, in the same ratio: 30% calls CompanyA, 30% calls CompanyB, and 40% calls CompanyC. Of course, there might be large unforeseen shocks that ruin my approach by making my call options go to USD 0, so that I lose my money. But apart from that, (1) is it reasonable to think that the same diversification effect that I expect in strategy 1 would also occur in strategy 2? And (2) what am I overlooking if I would invest in Strategy 2? ## Answer by Lars Wissler (score 0, accepted) https://quant.stackexchange.com/a/55285 Yes and no: diversification always decreases the effects of surprise events (unless they hit the whole portfolio equally) and as such the overall risk of extreme moves. That is true for option portfolios in the same way as it is for stock. But there is a key difference: stocks statistically increase in value so diversification in a stock portfolio decreases the probability/size of downward shocks and increases the probability of a steady uptrend. However, options statistically DECREASE in value. With options, you have to hit time and strike and if you hit right, you win big but usually you loose. So with a diversified long options portfolio your probability increases to get a steady DOWNTREND of your capital. Basically if you throw darts at the stock market, you win, but if you throws darts at the options market, you lose. Things might well be different building a diversified SHORT options portfolio. And obviously if you have a winning options strategy that can be applied with equal profitability across multiple underlyings, the risk of big one time shocks is decreased for the same reasons as in a diversified portfolio. Disclosure: I am affiliated with www.leeway.tech and have a personal interest in its success.
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