Global equity markets have rallied over recent months, but it is non-cyclical, defensive stocks that have led the charge.
Many analysts now warn that valuations on that part of the market are way out of line with historical patterns and could snap back, leaving investors who thought they were buying defensive companies stranded.
However Walls, manager of the five crown-rated Unicorn Mastertrust, says these stocks will continue to become more expensive as long as the Fed and the Bank of England's printed money keeps "sloshing" around the market.
"Managers that play the quality end of the market such as Nick Train, they have produced phenomenal returns."
"The question is, can those defensive-type companies continue to see their P/E ratios expand at such high levels?" he said.
"If you look where we are today compared with where we were six months ago, everything – except commodities – is more expensive. But it’s the defensive companies which offer decent yields that have led the rally."
"In the investment trust world, you get the danger of a double whammy. If a manager has been investing in those wonderful defensive names, then there is every likelihood that their shares will now be trading on a premium."
"You are almost better off going for an open-ended fund, but they keep soft-closing," he added.
This hunt for income and safety has caused star managers such as Sebastian Lyon and Steve Russell to voice concerns about overstretched valuations in some of the less market-sensitive yielding stocks, which could potentially cause a mass sell-off.
Simon Laing, manager of the Invesco Perpetual US Equity fund, recently told FE Trustnet he is upping his exposure to cyclicals as he feels that defensive names are now overbought.
However, Walls says investors have nothing to fear over the next few years as the rally in defensives still has plenty of legs.
"I wouldn’t like to be pinned down as to when this will stop. As long as central banks keep printing money and they see the state of the bond market, investors will lean towards defensive, yielding equities."
"This is the big problem I have with it, because the central banks just keep printing money. Eventually it will create a bubble."
"I’d imagine there will be a consolidation in the markers over the coming months and then it will resume again."
"There will be a point where investors need to think about fundamental ratings being overstretched."
"A bubble will appear, but it could be five years down the line," he added.
Walls has managed the £6m Unicorn Mastertrust, which is a fund of investment companies, since its launch in December 2001.
According to FE Analytics, it is a top quartile-performer in the IMA Flexible Investment sector over one, three, five and 10 years.
Performance of fund vs sector over 10yrs
Source: FE Analytics
Unicorn Mastertrust is the second-best performing fund in the sector over the past decade, with returns of 217.57 per cent.
The only portfolio to have beaten it over this time is FE Alpha Manager Toby Ricketts' Margetts Venture Strategy fund.
Alan Miller, chief investment officer at SCM Private, takes the opposite view to Walls.
He warns investors against assuming that the performance of an asset class in the past will continue.
"A basic fact of investing is that your future return is actually determined more than anything by the price you pay for something – not whether its earnings, share price or chief executive’s hairstyle or anything else happens to remain unchanged," he said.
"If you invest in a stock with a very high valuation and very low growth you are a) not likely to make much money and b) could easily lose a lot of money when the hot money disappears."
"As gold has recently showed, investing in an asset not supported by fundamentals may not be such a safe strategy."
"The fact that some stock or asset has not changed much in price recently does not prevent it from falling considerably in the future," Miller added.
Valuation is something that Walls has to constantly think about in his fund, as discount volatility can have a huge effect on the returns made from investment trusts.
He says that the whole market is looking more and more expensive these days, making it harder to stick to a valuation discipline.
"Something like Murray International is now trading on a premium of 11 per cent. It is a very good fund, but I don’t hold it as I find it generally difficult to buy a trust on a premium," Walls said.
"I don’t think I have ever knowingly bought a trust on a premium. I hold a few now that are on a premium, such as Baillie Gifford Japan and Baillie Gifford Shin Nippon."
"Japan has done very well so far this year so I have been scratching my head deciding on what to do, but I met with the management team and I was glad to see that underlying valuations in their portfolio still look attractive."
"In this market, the parameters have changed a little bit as there has been more interest in investment trusts on the back of RDR."
"Also, management teams are tightening their discount-control mechanisms and others are implementing zero-tolerance discount control."
"There has been a general narrowing up in average discounts, so maybe I might have to be a bit more flexible towards both premiums and discounts," he added.
Unicorn Mastertrust requires a minimum investment of £2,500 and has an ongoing charges figure (OCF) of 1.61 per cent.