Stocks have soared of late, with United States indices hitting all-time high after all-time high. Various bearish arguments – some questionable, some downright erroneous – invariably do the rounds when stocks are flying high. Expect to hear the following over the coming weeks and months.

New highs are bad

One can see why investors get nervy around all-time highs. Anyone who bought the S&P 500 at the market top in March 2000 would have had to wait seven years before hitting their break-even point. Not long after new highs were finally set in late 2007, another crash ensued; stocks did not reclaim their 2000 high until 2013, a 13-year drought.

The recent spate of all-time highs – the Dow Jones Industrial Average hit new highs seven days in a row – means many investors have a sense of vertigo. While that’s understandable, it makes no sense to automatically see new highs as symptomatic of a dangerous market that has gone too far. After all, stocks tend to rise over time, so they’re going to spend a lot of time hitting all-time highs.

In his book A Wealth of Common Sense, Ben Carlson notes that the S&P 500 has hit more than 1,100 new highs since 1950 – equivalent to almost 7 per cent of all trading days, or roughly one day in 15.

The noughties were atypical in that respect – just 13 all-time highs were registered, even less than the similarly barren 1970s. However, the S&P 500 spent more than quarter of time hitting new highs during the 1990s and again during the 1960s, when 306 and 288 all-time highs were respectively registered. There were 192 new highs (17.3 per cent of trading days) in the 1980s and 205 new highs (18.5 per cent) in the 1960s.

Between 2013 and May 2015, new highs again became a regular occurrence, with 108 highs registered over this period. A 14-month-long trading range then took hold, only for stocks to convincingly break out to fresh all-time highs last month. Far from being a warning sign of an overheated market, this is a bullish signal: the historical data indicates that the more new highs the better, with such periods associated with long bull-market environments.

The moral, as Reformed Broker blogger Josh Brown bluntly noted last year, is that "anyone who tells you that new highs are abnormal or a reason to sell is a fool".

Ageing bull

The current bull market is more than seven years old, making it the second-longest rally in history. "While there's no rule that bull markets die of old age", Time magazine cautioned recently, "there is a feeling that after a seven-year run in which stocks have gained 200 per cent, equities may be due for a downturn, if not a rest".

This lazy thesis has been advanced countless times in recent years. Firstly, as Time admits, it's certainly true that bull markets don't necessarily die of old age – the longest (1987-2000) lasted 13 years. Secondly, stocks almost satisfied the official definition of a bear market – a fall of 20 per cent – in 2011, when the S&P 500 fell 19.4 per cent. In fact, stocks actually suffered a peak-to-trough decline of 21.6 per cent in 2011, if one uses the intraday low registered at the market bottom on October 4th, as opposed to the index's daily closing price. In other words, one could just as easily argue the current bull market is less than five years old, as opposed to being an ageing seven-year old.

Thirdly, bear markets have the effect of purging markets of excess and speculation; by shaking out the weak hands, this sets the scene for future gains. However, corrections can serve the same function, and the current bull market has certainly seen its fair share of shakeouts – if intraday prices are used, there have been six double-digit corrections since 2009. Indeed, there is a case to be made that stocks have just emerged from an environment that was a bear market in all but name.

Equities went nowhere over an 18-month period; two double-digit corrections occurred during that period while the MSCI world index fell into an official bear market, catalysing no shortage of apocalyptic commentary; investors’ patience was exhausted, with sentiment surveys displaying levels of bearishness typically seen at bear market lows; and the average stock suffered a 34 per cent decline between May 2015 and February 2016, with indices being propped up by a small number of large-cap stocks.

Finally, while the current bull market may be a long one, it has not been a remarkably strong one – having gained almost 220 per cent since March 2009, it ranks fourth in terms of percentage gains, behind 1982-1987 (229 per cent), 1949-1956 (267 per cent) and 1987-2000 (582 per cent).

Note too that the S&P 500 has “only” doubled since October 2011’s bottom; if one dates the bull market back to that period, then it starts to look like a minnow compared with the biggest rallies.

Defensive leadership is ominous

Defensive rather than cyclical stocks have led stocks higher in 2016. This ominous market behaviour apparently indicates a downturn lies ahead.

However, there’s nothing strange about defensive leadership following corrective periods. In similar market environments in the past, defensives led the gains on 70 per cent of occasions.

Besides, defensives are certainly not the only gainers: market breadth has been very strong in recent months, with 87 per cent of stocks recently trading above their 50-day moving averages.

Overvaluation means stocks must slip

It’s easy to argue that stocks are overvalued. The S&P 500 trades on 17.1 estimated earnings, according to FactSet, well above its five-year (14.6) and 10-year averages (14.3).

Worse, the S&P 500’s cyclically adjusted price-earnings (Cape) ratio, a widely followed measure that averages earnings over 10 years, is 26, a level exceeded on only three occasions – in 1929, 2000 and 2007, all prior to major market crashes.

Bulls would counter that structural market changes have resulted in Cape ratios rising in recent decades – the S&P 500 has traded on an average Cape ratio of 25 over the last 25 years, according to JPMorgan data, which indicates today’s valuations are not as extreme as they may seem at first glance.

However, even if one rejects bullish rationalisations for the high Cape reading, one should be very careful of extrapolating that stocks must slip on the basis that they appear overvalued.

Valuation metrics such as Cape are a good indicator of long-term returns; as a general rule, high valuations are typically followed by low returns, whereas low valuations tend to be followed by high returns. However, valuation is almost useless as a market-timing measure: it should not be used to forecast corrections or 12-month returns.

High valuations merely indicate that future returns will be lower than historical returns – that’s all.

Low Vix indicates market complacency

The Vix, or fear index, is extremely low at the moment. Whenever low Vix readings are registered, the tired “markets are complacent” complaint gets trotted out. In reality, while the most elevated Vix readings are associated with higher future subsequent returns, the inverse is not true.

Data shows the lowest decile of Vix readings tend to be followed by 12-month returns that are roughly in line with historical returns. Similarly, low Vix readings can persist for years – they should not be viewed as periods of unsustainable market calm.

Markets are ignoring stagnant earnings

It’s true that earnings are at risk of declining for the fifth consecutive quarter. However, it’s hard to argue markets are ignoring the earnings picture; after all, the profits recession was the main reason that stocks were stuck in a 14-month trading range following May 2015’s peak.

The recent breakout to fresh highs indicates markets, which are always forward-looking, expect an earnings turnaround will come sooner rather than later.

If that turns out to be untrue, then stocks may well retreat. However, breakouts of long trading ranges tend to be sustained, indicating that a profits upturn may finally be on the horizon.