The holding company discount is different from the conglomerate discount and the liquidity discount. It can be defined as follows: a holding company trades at a discount when its market capitalisation is less than the sum of the investments it holds, which it usually is. Thus, a holding company will have a book value of equity of 100, although its market capitalisation will be 80. This means that the investor which buys one share in this holding company thinks that he's got a good deal since he paid 80 for something that's worth 100, although this value will never be achieved since the holding company will always be discounted unless it is liquidated. You should thus value each of the parts of the holding company and compare the results with the market capitalisation of the holding company.

The discount can disappear, following a merger between the holding company and the operating subsidiary, for example. I don't see how listing the subsidiaries could reduce the discount, on the contrary. A spin-off is the distribution of the shares of a subsidiary. It may reduce the discount but not eliminate it, since what remains in the holding company after the spin-off (discounted cash?). If shares are bought back, the holding company's cash can be paid out but this doesn't make the discount go away, as, it may make the holding company shares even less liquid.

For more information, see chapter 41 of the Vernimmen.