If Woo is buying Wheelock shares for the first time in a long time, he must think them undervalued. Is the stock still a good buy despite having almost doubled this year and near its highest levels since 1997?

Probably not, but to get to that view, potential investors should consider two points. First, look at how much Wheelock is discounted relative to the fair value of its underlying assets. This is the conglomerate discount.

Second, consider the percentage of Wheelock's value that is made up of its separately listed businesses. If nearly all of a conglomerate's worth consists of businesses that are separately listed, investors have fewer reasons to buy the shares of the parent. Better to buy the underlying stocks, getting closer to the profits and dividends of the underlying businesses.

In a nutshell, the greater the value of a conglomerate that can be bought by buying the stocks of its listed assets, the higher the conglomerate discount should be. One must consider the conglomerate discount to the proportion of fair value that is captured by underlying listed stocks.

These are subtle points, so please bear with me.

Let's begin by taking a closer look at Wheelock. Woo owns 60 per cent of the conglomerate, which has served as the family vehicle to control the larger Wharf Holdings, in which it has a 50.02 per cent shareholding. Wharf's interests include Hong Kong and mainland properties and ports, and i-Cable and other telecommunications.

Wheelock also owns 76 per cent of Singapore-listed Wheelock Properties, known for its high-end property developments in the city. Wheelock has become more active in property development in Hong Kong, with projects at Lexington Hill, Kadoorie Hill and the Austin MTR station, among others, according to its interim report.

The current market value of Wheelock's interest in Wharf - about HK$92.3 billion - already exceeds Wheelock's market capitalisation of around HK$79 billion. The stake in Wheelock Properties is worth another HK$10.9 billion.

Wheelock's businesses outside Wharf and Wheelock Properties could be valued at about HK$6 billion based on, say, a 40 per cent discount to book value as of the middle of this year. Adding Wheelock's stakes in Wharf and Wheelock Properties, which have a total market value of HK$103.2 billion, Wheelock has a fair value of about HK$109.2 billion, implying a fair value per share of HK$53.84.

Wheelock's closing price on Wednesday was HK$38.90, which indicates investors discount the conglomerate by 28 per cent.

This suggests value. However, with about 95 per cent of its fair value attributable to listed Wharf and Wheelock Properties, investors have little reason to invest directly in Wheelock. If they want exposure to its underlying businesses, they can buy those two underlying stocks.

Let's compare Wheelock with the conglomerates that were covered previously in this column. Their fair value can be calculated in part by referring to the market value of their stakes in listed companies.

In addition, the fair value of the unlisted property assets of Henderson Land, New World and Shun Tak development could be determined by applying a similar 40 per cent discount to book value.

The results show a trend: the higher the percentage of a conglomerate's value that is captured by the underlying stocks, the more investors discount the conglomerate stock in relation to its fair value. (See graph.)

In other words, an investor would be motivated to buy the conglomerate stock only if it holds a lot of assets not owned by its listed subsidiaries, as the stock would be the only way to get exposure to these assets.

This is a long way of saying that despite the discount in Wheelock's share price to its fair value, there may not be much upside in buying the stock, as the current discount of 28 per cent is starting to look a little tight.

Indeed, Wheelock is a notable outlier on the graph. Its conglomerate discount is small considering the parent has few assets that are not captured by its listed subsidiaries.

The implication is that Wheelock is not such a bargain. This argument becomes stronger when you consider the stock used to be much cheaper. At the beginning of last year, Wheelock's discount to fair value stood at 38 per cent. At the start of this year, it was 41 per cent.

When you compare it with other conglomerates, it seems that Wheelock ought to be trading at a larger discount to fair value, as its separately listed assets contribute to a substantial portion of that fair value.

Wheelock's narrowing fair value discount is mainly due to its share price outperforming that of Wharf (the dominant contributor to Wheelock's fair value and profitability), which increased by a more modest 71 per cent this year. This is probably explained by the fact that Woo has been actively buying Wheelock shares since August last year.

Finally, any investor looking to buy Wheelock on the expectation that it will be soon privatised will probably be disappointed. If Woo were planning a privatisation, he would not be driving up Wheelock's share prices through a series of stock purchases.

It would make more sense for him to make a one-off offer to shareholders when the Wheelock share prices were lower.

Assuming Woo did buy out Wheelock's minority shareholders at, say, a 30 per cent premium to market price and this was funded entirely with debt, Wheelock (excluding listed Wharf and Wheelock Properties) would end up with a net debt (cash minus debt) of about half its fair value, which would be hard to service with the dividends from its listed subsidiaries.

Which all suggests that the Wheelock stock, despite its recent frothy price gains and insider buying, may not be such a hot stock.