If you have shares in a fund (irrespective of stratgey) you have no claim on the underlying assets or earnings. What you have is a share in the economic performance of the fund as a legal entity. It might seem like splitting hairs but it's actually important. Every fund, whether long only or something with a more esoteric strategy, continuously changes its portfolio. Therefore as investors come in and out of the fund, in order to provide a fair valuation of the fund, the fund recalculates its current total value by assessing the current market price of its investments/assets ("mark to market") and dividing by the number of outstanding shares or units. That value is used to issue new shares or repay people leaving the fund.
You are spitting hairs. Anyone who invests in a fund and reads the prospectus is or should be aware of this.
That process is exactly the same for long only funds as it is for more exotic straetgies; long-short, total return etc.
The process by which a fund actually establishes a unit price may be equivalent, but you're not investing in the same things. Investing in a hedge fund is not the same as investing in conventional asset classes. If the OP was told or given the impression that regular investments in a hedge fund is the equivalent of regular investments in an asset class (i.e. productive assets the share common characteristics) he has been poorly advised.
One rationale for regular investing in an asset class is (a) the tendency for asset classes to mean-revert; and (b) the propensity of assets to increase in value over time due to e.g. increased earnings power, scarcity, etc. As hedge funds are not an asset class they do not so express mean-reversion; and as they are a series of trades, e.g., long/short, equity market neutral, global macro, convertible arbitrage, etc., they have no inherent earnings power or scarcity value.
Furthermore, the return on individual assets is essentially (a) compensation for the risk of investing in the asset class and (b) compensation for the risk of holding the individual asset. The latter is 'alpha ' risk that is diversified away within the asset class and you are left with non-diversifiable risk or 'beta'. As you have diversified away alpha risk you have also removed the reward for the risk of holding it. Hedge funds, by their investment strategies, aim to maximize the return for holding alpha risk. That's why you invest in them – to obtain the rewards associated with holding alpha risk. So by making regular investments in a hedge fund the OP is in essence buying alpha risk. But as he appears to have only one fund – the hedge fund – he has no beta risk and is missing the rewards associated with holding it. I doubt this is a good investment strategy.
These may be blanketed with the term "hedge funds" but it's such a broad term that it is effectively meaningless. It was originally meant to describe a strategy that was a hedge against regular market volatility. Some hedge funds are extremely low volatility so have a place in a portfolio. But to describe them as "a series of bets" misundertands them.
'Bets' is a colloquial expression for such strategies.. One fund in which I invest says in the first line of its prospectus “This fund invests in trades.” It can't be clearer that that. If the Financial Times can use the term 'bets' it in relation to certain hedge fund strategies
https://www.ft.com/content/bfab7d66-91d4-11e9-b7ea-60e35ef678d2 are you suggesting the FT misunderstands hedge funds?
Your original point that an investor in a long only fund is buying into the claims on the underlying asset is not strictly true. But I understand how a holding of an equity position in a long only fund might seem more tangible than, for exmaple, a foreign exchange position... or a spread position "long Volkswagon / short Tesla" (to use a topical discussion on these boards). But actually they are all the same for a fund investor. When you buy shares in the fund, you share the economic benefit from the current and future investment positions in the fund from that date forward (you don't obviously gain any benefit from the historic performance of those positions).
Investment companies do not market their products in such terms. Zurich Life e.g.. says straight out that their funds “offer investors the opportunity to invest in a concentrated portfolio of stocks, chosen and actively managed by Zurich Life”. To any average Joe this is an offer to obtain the rewards associated with investing in a selected group of stocks. And investing in its most basic definition is establishing a claim on the performance of an asset. Otherwise nobody would do it.