CEF Portfolio Concentration vs. Yield

The way I was trained in credit, i.e. where there is default risk, is that since investors are only getting back par plus coupons there should be a strong bias toward reducing large losses.  This goal is achieved by lending in a way that defaults are not correlated (avoiding loading up on overlapping sectors, regions etc.) as well as portfolio size diversification so that idiosyncratic risks are reduced as well. 

This doctrine is different than equity investing, where there are much larger payoffs to portfolio concentration, since investors enjoy unlimited upside, and do not have good investments forcibly paid back (like a callable bond).

In that vein, I ran some numbers to compare the yields of CEF's I follow vs. a simplistic measure of their portfolio concentration (as a proxy for that risk of a large loss).  I pulled the sum of percentages of each funds top 10 positions.  That may not truly capture the risks as some funds (particularly those that use derivatives/govt bonds extensively) will show up as artificially riskier under this measure.  But I think, in the main, it's illustrative of the portfolio construction, and risks assumed, of the various management teams. 

My bias, all things being equal between yields, is to prefer the more diversified holdings.

Closed End Funds
	Name	Yield	Conc
JFR	NUVEEN FLOATING RATE INCOME	7.51	16.59
EFT	EATON VANCE FLOAT RT INC TR	6.54	8.74
BGT	BLACKROCK FLT RT INC	6.46	13.43
BSL	BLACKSTONE/GSO SENIOR FLOAT	6.86	11.46
FCT	FIRST TRUST SENIOR FLOATING	6.78	11.06
PPR	ING PRIME RATE TRUST	7.24	16.91
VVR	INVESCO VAN KAMPEN SENIOR IN	6.58	11.45
DVF	BLACKROCK DIVERSIFIED INCM S	6.86	12.09
AFT	APOLLO SENIOR FLOATING RATE	6.94	#N/A N/A
GDV	GABELLI DIVIDEND & INCOME TR	6.07	13.99
MGU	MACQUARIE GLOBAL INFR TOT RT	5.33	43.74
UTF	COHEN & STEERS INFRASTRUCTUR	8.21	29.36
RVT	ROYCE VALUE TRUST	5.91	7.89
USA	LIBERTY ALL STAR EQUITY FUND	6.91	19.34
LGI	LAZARD GLOBAL TOT RT & INC	6.80	30.98
EVT	EATON VANCE TAX-ADV DVD INC	7.92	19.80
NIE	AGIC EQUITY & CONVERTIBLE IN	6.64	19.33
GLO	CLOUGH GLBL OPPORTUNITIES FD	9.94	52.65
BDJ	BLACKROCK ENHANCED EQUITY DI	9.43	21.09
EOS	EATON VANCE ENH EQT INC II	9.96	36.09
ETJ	EATON VANCE RISK-MANAGED DIV	10.95	28.76
EXG	EATON VANCE TAX-MANAGED GLOB	11.67	19.89
JPZ	NUVEEN EQUITY PREMIUM INCOME	8.88	22.97
JSN	NUVEEN EQUITY PREM OPP FUND	9.26	28.63
NFJ	NFJ DVD INTEREST & PR STRAT	10.50	25.32
DBL	DOUBLELINE OPPORTUNISTIC CRE	7.45	25.44
JMT	NUVEEN MTG OPPORT TERM FUND	8.41	15.58
DMO	WESTERN ASSET MORTGAGE DEFIN	8.06	10.26
JLS	NUVEEN MORTGAGE OPPORTUNITY	8.45	18.58
FMY	FIRST TRUST MORTGAGE INCOME	9.75	42.82
EHI	WESTERN ASSET GLOBAL HIGH IN	8.67	11.92
FLC	FLAH & CRUM/CLYMORE TOT RET	8.65	29.46
JPS	NUVEEN QUALITY PREFERRED II	7.24	21.51
JHS	JOHN HANCOCK INCOME SECS TR	6.92	19.37
HPS	JOHN HANCOCK PFD INCOME III	7.63	27.53
ACG	ALLIANCEBERNSTEIN INC FUND	5.73	54.36
AWF	ALLIANCEBERNSTEIN GL HI INC	7.97	9.52
LBF	DWS GLBL HIGH INCOME FD INC	6.07	30.60
GDO	WESTERN ASSET GL CORP DEF OP	7.92	11.64
BNA	BLACKROCK INCOME OPPTY TRST	6.24	59.59
BPP	BLACKROCK CREDIT ALLOC III	6.64	24.76
BTZ	BLACKROCK CREDIT ALLOC IV	7.08	24.26
PSW	BLACKROCK CREDIT ALLOCAT I	7.03	26.28
PSY	BLACKROCK CREDIT ALLOCAT II	6.76	21.45
MCR	MFS CHARTER INCOME TRUST	6.66	11.15
MMT	MFS MULTIMARKET INC TRUST	6.73	10.94
JQC	NUVEEN CREDIT STRATEGIES INC	8.69	16.68
MTS	MONTGOMERY ST INCOME SEC INC	3.72	45.87
ICB	MORGAN STANLEY INCOME SECS	4.61	15.74
BHK	BLACKROCK CORE BOND TRUST	6.03	56.36
JPC	NUVEEN PREFERRED INCOME OPPO	8.20	22.04
GCF	GLOBAL INCOME & CURRENCY	6.84	61.16
ERC	WELLS FARGO ADVANTAGE MULTI	7.85	16.70
CSQ	CALAMOS STRAT TOT RETURN FD	8.57	26.41
GDF	WESTERN ASSET GLOBAL PARTNER	9.37	17.87
EDD	MORGAN STANLEY EMERGING MARK	7.50	71.62
CHW	CALAMOS GLOBAL DYNAMIC INCOM	8.70	12.39
TEI	TEMPLETON EMERG MKTS INC FD	6.13	35.58
PHK	PIMCO HIGH INCOME FUND	10.66	45.53
PCM	PIMCO COMMERCIAL MTG SECS TR	8.57	36.03
PDI	PIMCO DYNAMIC INCOME FUND	8.24	#N/A N/A
PKO	PIMCO INCOME OPPORTUNITY FUN	8.36	31.28
PFN	PIMCO INCOME STRATEGY FD II	9.08	33.68
PFL	PIMCO INCOME STRATEGY FUND	9.01	35.31
RCS	PIMCO STRATEGIC GLBL GOVT	8.26	26.94
PCN	PIMCO CORPORATE & INCOME STR	7.96	37.55
PTY	PIMCO CORPORATE & INCOME OPP	8.13	26.10
GOF	GUGGENHEIM STRATEGIC OPPORTU	8.68	27.37

Some things that stuck out to me:  how much idiosyncratic risk the PIMCO CEF's tend to have. (Just punch up some of their holdings list to see what I'm talking about)  I realize they have excellent credit analysts, but one can compare a typical HY offering in their lineup to something like Alliance's HY funds and see that there is much more security selection diversification in the A-B product -- albeit at a cost in yield.  What I find a little odd is that for a shop that prides itself on macro calls (PIMCO secular forum and all that...) they are using their security selection expertise in driving their strong FI CEF performance. It comes down to what you are looking for in your CEFs -- security selection conviction or portfolio diversification.  The average concentration number across the funds I'm tracking (clearly many kinds) is 26%.

==================

Just to clarify what my proxy for the idea of large loss is very simply: concentration risk = sum of top ten positions percent weight.

For example, looking at PFN:

BACR 14 11/29/49	BACR	5.556
AIG 8.175 05/15/58	AIG	4.821
PNC 12 12/29/49	PNC	3.768
NTHRN CA PWR-TXB-B-LO	NORPWR	3.194
COBKAC 11 12/31/49	COBKAC	2.982
RABOBK 6 ⅞ 03/19/20	RABOBK	2.858
PPL 9 ½ 07/01/13	PPL	2.806
WFC 7.98 03/29/49	WFC	2.657
AIG 6.765 11/15/17	AIG	2.556
AMERN MUN PWR-B-BABS	AMEPWR	2.487

PFN's concentration is the sum of the final column: 33.68%

Adding more funds -- that do not have overlapping portfolios -- will reduce the concentration risk across one's holdings.  This can be an argument for diversifying across multiple management companies.  

I'm trying to figure out how to get a portfolio VaR* and then compare that to the yield, but that only covers the NAV, ...and I can't automate that into a spreadsheet.  One can look at long run comparisons of market price volatility to NAV volatility and scale them, as well.  

*VaR has lots of issues too I know.

PS: I've run some sample numbers on VaR and CVaR, which are not perfect, since CEF holdings do not get modeled in toto, but they loosely line up with the concentration numbers.  That is: funds with high concentration metrics seem to show higher VaR numbers for their portfolios.  That makes intuitive sense.