* Large numbers of young workers can boost growth -study
* But "youth club" countries may not join mainstream soon
* Markets lack size and liquidity
* Unease grows over Zimbabwe after Mugabe party victory
* Zambian bond has underperformed due to weak copper price
* Rwanda scores better but has only two listed stocks
By Carolyn Cohn
LONDON, May 19 (Reuters) - Three members of Africa's "youth club" - Rwanda, Zambia and Zimbabwe - offer some of the fastest-growing working populations in the world, if only investors can capitalise on that.
If the countries' demographic trends can be coupled with good education to create skilled jobs and an avoidance of political unrest, this should lead to economic growth quickly enough to attract portfolio investors, some analysts say.
None of the three makes it to the flagship frontiers stock index, which tracks exchanges a tier below the larger, more established emerging markets. But according to United Nations projections, their working-age populations will increase by up to 20 percent by 2020.
This is attracting investors' attention, even though the precise effect of expanding populations of young workers on economic growth remains contested.
"I have never paid attention to demographics because I didn't think it could be relevant on any investor timeframe - I was wrong," said Charles Robertson, chief economist at Renaissance Capital.
Renaissance recently published a study of frontier markets showing Rwanda - which hosts the African Development Bank annual meeting this week - along with Zambia and Zimbabwe as the top three countries for demographics.
Each 1 percentage point annual rise in the working-age population should equate to a 1 point improvement in the annual growth rate, Robertson said. In the case of Rwanda, demographics would account for an extra 4 percentage points a year on growth.
But unsophisticated financial markets and, in some cases, erratic government policies may keep these countries out of the mainstream for some time to come.
"Liquidity is a big constraint," Robertson added.
Around $22 billion in funds is under management in frontier markets, according to Rencap estimates, mostly through the MSCI frontiers index, one of the best-performing markets this year.
Following the upgrading of two big Gulf markets - Qatar and United Arab Emirates - to emerging market status this month, Africa will make up around 30 percent of the frontiers index. But even to make it to frontier stock market status requires levels of size, liquidity and market access which the youth club three don't have.
Of the three, Zimbabwe has the largest and most-established stock market, which became a favourite with frontier investors last year, hitting record highs. But even here, daily turnover of a few million dollars compares with around $25 million in frontier market Nigeria, for example.
Stock favourites include brewery company Delta Corporation , and mobile phone operator Econet Wireless.
Zimbabwe averaged nearly double-digit annual growth between 2009 and 2012 as it recovered under a power-sharing government from economic collapse. But rates have fallen sharply due to shortages of electricity and capital, while less than 20 percent of the working population is in formal employment.
Investors have also become more uncomfortable since elections last year cemented President Robert Mugabe's Zanu-PF party in power. "We still have some exposure to Zimbabwe but we are less bullish on Zimbabwe than we have been," said Andrew Lister, fund manager at Advance Emerging Capital.
Zimbabwe, shunned by Western governments and funding institutions, has not been able to follow many other African nations in issuing international bonds.
For Danat Abdrakhmanov, institutional portfolio manager at Eaton Vance, a growing population is not enough for investment. "In terms of the way we look at countries - we want to see rule of law, less regulation, less government, smarter regulation - when you are talking about countries like Zimbabwe, things can only improve," he said.
Valuations are also not as cheap as they once were, with price-earnings ratios at 11 for the MSCI Zimbabwe index, according to Datastream, compared with a little over 12 for the MSCI emerging markets index.
Zambia was one of the forerunners among African countries to issue international debt, launching a $750 million bond in 2012.
The bond has not been a great success, with weakness in the price of copper - Zambia's main export - leading Zambia to underperform other African debt. (For GRAPHIC on African debt performance, see http://link.reuters.com/set57v)
Zambia succeeded in issuing a second bond this year, though at a higher yield.
Zambian-focused mining companies listed outside the country, such as First Quantum Minerals and Gemfields, have attracted investors. But illiquid local stock markets, a sliding currency and a worryingly large budget deficit have kept many international investors away.
"Zambia has some issues," said Stuart Culverhouse, chief economist at frontier markets broker Exotix. "It had a fiscal blow-out last year and the currency has come under a lot of pressure. It has to make sure it does not repeat that."
Rwanda scores better than the other two countries for ease of doing business and low levels of corruption and debt, and Rencap flags it as a buy.
Critics accuse President Paul Kagame of being authoritarian and trampling on media and political freedoms, accusations he denies. However, Kagame has won international praise for progress in his attempt following the 1994 genocide to transform Rwanda into a middle-income country by 2020.
The country launched a debut dollar bond last year at a yield below 7 percent, which has performed well.
Investors are eager to get into Kigali, but for fund managers there is even less to buy than elsewhere. The stock market boasts only two companies - brewery company Bralirwa and Bank of Kigali - though expectations are for more to list this year.
The lack of investible instruments reflects the drawbacks with focusing on population growth alone.
"I would never trade demographics," said Stephen Bailey-Smith, head of African research at Standard Bank. "There is going to be growth from demographics, but you have a huge number of people chasing a limited amount of liquidity - the demographic premium gets priced in in two seconds." (Additional reporting by Natsuko Waki; editing by David Stamp)